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In 1991, the Soviet Union ceased to exist as a country and the land was divided up into 15 countries, generally along boundaries of countries that existed when the Soviet Union formed in 1917, swallowing up existing countries that had been under Russian control. But this is overly simplistic and boundaries/countries were not the same as before.

Yugoslavia also broke into multiple countries around the same time (for related reasons). There were wars over this but the divisions in some cases were not the result of war but rather the cause.

In 1993, Czechoslovakia split into the Czech Republic and Slovakia.

It is sometimes known as the Velvet Divorce, a reference to the
bloodless Velvet Revolution of 1989 that led to the end of the rule of
the Communist Party of Czechoslovakia and the restoration of a
capitalist state in the country.

Vatican City, "an independent city-state enclaved within Rome, Italy" was given peacefully to the church by Italy in 1929.

And these are just a few examples from 20th century Europe. There are more in other places and times.

Even if there were not, it's something you could have in your story. The threat of war may be enough to convince a country to give up land for another country. Or it could be economic sanctions. Or the promise of economic benefit. Religion. A desire for peace. A vote of the people to secede (as Britain is (sort of) doing from the EU. Or any of multiple other reasons.

it seems almost impossible for a country to give up land for a new country.

Not necessarily. There are also example of peaceful separation: Czechoslovakia is one of these.

Czechoslovakia was a sovereign state in Central Europe that existed from October 1918, when it declared its independence from the Austro-Hungarian Empire, until its peaceful dissolution into the Czech Republic and Slovakia on 1 January 1993.

From 1948 to 1990, Czechoslovakia was part of the Eastern Bloc with a command economy. Its economic status was formalized in membership of Comecon from 1949 and its defense status in the Warsaw Pact of May 1955. A period of political liberalization in 1968, known as the Prague Spring, was forcibly ended when the Soviet Union, assisted by several other Warsaw Pact countries, invaded. In 1989, as Marxist–Leninist governments and communism were ending all over Europe, Czechoslovaks peacefully deposed their government in the Velvet Revolution; state price controls were removed after a period of preparation. In 1993, Czechoslovakia split into the two sovereign states of the Czech Republic and Slovakia.

I read your question two different ways. If you're asking about the general process required for creating a new country peacefully, then it would look much like the non-peaceful route (just without the violence). Boundaries would have to be defined and a government set up. Becoming a "real" country won't happen until other countries formally recognize you, build a diplomatic mission, etc. Having your former parent country be the first to formally recognize you would go a long way towards cementing your new country's legitimacy, and would help assuage any other nations' fears about stepping into the middle of another country's internal problems.

If instead your question is more along the lines of "how could I ever convince a government to do such a thing", then it's a bit more tricky. Most politicians have far too much pride to voluntarily let go of part of their territory. There are some circumstances, though, where I could see a reasonable government choosing to do this sort of thing. You'd rarely find a country eager to do that, but there are many cases where the alternative could be much worse.

• 
  Avoiding a war - The territory in question is - and has been - hotly contested territory with a neighboring country. Ownership of that region has changed hands multiple times, and always as the result of a war. Neither side really wants the region all that much, they just really don't want the other side to have it. After a decade of negotiations, both sides agree to spin that region off into an independent country under the condition that it must remain fully independent of either nation.


• 
  Logistical expediency - Imagine if the modern UK consisted of five constituent countries: England, Wales, Scotland, Northern Ireland, and Australia. Administering Australia from the other end of the planet would be tremendously expensive and difficult. The only way to ensure that Australians had the type of responsive government they need would be to have special local Australian-run branches of the court systems, law enforcement, etc. Your country eventually realizes that it would be better - and cheaper - for all involved if they formally spun off Australia into a fully-independent state (after all, you're most of the way there already). There's no hard feelings and the two remain close allies, but there are no longer any dependent relationship between them.


• 
  Dissolution of a temporary condition - Decades ago, a fairly powerful country in the region was taken over by a brutal dictator who built up his military and sought to conquer most of the region. The dictator was just barely sane enough to know not to attack your country, though. You were large and powerful enough that he knew he couldn't win that fight. One of your neighbors is a long-time ally and critically-important trade partner. Unfortunately, they're a smaller nation and don't have much of a military, and found themselves a prime target of the dictator. Your ally agreed to let you annex their territory so that the dictator wouldn't dare attack them, but they only loosely integrated into your overall government. After decades of keeping the madman at bay, he was finally deposed the threat is gone. The need for protection is over, and your former ally wishes to return to being an independent nation.


• 
  Cultural/ideological split - Your country is rather large, both in terms of size and population. Over time, your country has developed rather distinct regional cultures with different sets of values. This is causing havoc in your legislature, as the increasingly different ideologies lead to nothing but disagreements, dysfunction, and a growing dissatisfaction with the government's performance. Your leaders conclude that there's no way to satisfy such a diverse group of needs with a single top-down solution. Splitting the nation into several smaller nations would allow each region to govern themselves in accordance with their particular needs, values, and culture, without having to force the other regions to do something they don't want to do. The new countries are self-determinate, but remain friendly and in a loose alliance.


• 
  Concession for a greater purpose - Your country was a member of a regional free-trade alliance for decades. Over time, this alliance has outgrown its original intent and become more of a government unto itself, and your people demand that your nation break free and regain its sovereignty. There's a big problem, though. One historically-poor region of your country has spectacularly prospered under the alliance's trade rules. Leaving the alliance would thrust them back into poverty, destroy their economy, and cripple the supply chains of every industrialized nation in the region. Your politicians have come up with an endless stream of terrible solutions for the problem of leaving the alliance. The only one that isn't completely bonkers is for this region to be spun off into an independent country that can choose to remain part of the trade alliance.

The process of balkanization is certainly very messy, but not necessarily bloody. Regions can vote themselves out via the democratic process, similar to the Scottish referendum. A colony, region or far out island territory could be abandoned for various reasons. Territories are sometimes sold like the Louisiana Purchase.

It turns out that this has already happened lots of times from developed nations over the past century.

Some examples to consider:

• Canada


• Australia


• New Zealand


• The Philippines


• Palau


• The Federated States of Micronesia


• The Marshall Islands

In all of these cases, the basic formula was some variation on the following:

• Form a stable local territorial/provincial government.
  
  Ideally, one that the power from which you wish to secede considers to be in line with its views on how a stable government should be run. For example, if seceding from the U.S. or U.K. within the last roughly a century, having a stable democratic republican form of government certainly helps the argument for independence.




• Keep asking to take on more power/responsibility locally.
  
  As your local government becomes more stable and increases its record of stability, continue asking the country from which you wish to secede for more local responsibility over running your territory's affairs, along with the power needed to carry out those responsibilities.




• Maintain good relations with the government from which you wish to secede.
  
  Maintaining good relations certainly helps when arguing for independence. The government tends to be much more likely to grant local powers and tends to be much more amenable to granting independence when the local government is working with it in a friendly manner rather than antagonizing it in an adversarial manner. It also tends to be more likely to grant those powers when it trust the local government not to use those powers to suddenly start acting significantly against its interests.




• Develop an independent national identity and culture.
  
  Of course, one of the key ingredients in getting independence is the local people actually wanting independence and beginning to think of themselves more as a separate nation and culture from the country from which secession is desired (if that's not already the case.) Over time, this also tends to get the rest of the people in the country from which you wish to secede to start thinking of you that way, too. And it makes the argument that you can form a stable sovereign nation after independence much stronger.




• Ask for independence.
  
  This step should be obvious, but, having completed the above steps, ask (ideally nicely) for independence. This often involves a significant degree of negotiating. It also sometimes involves initially being told no. When that happens, keep asking and keep negotiating. Going back to the first point, this is also often done in steps in order to ensure a smooth and stable transition of power. In some cases (Canada and Australia, for example,) asking for more and more local power may result in the local government eventually acting as a de facto sovereign nation well before the final vestiges of control by the government from which you are seceding are relinquished.

For such a scenario, there are two most important factors:

• Do you have approval of the government/overlord?


• Do you have popular support within the whole populace?

If you have government approval, you face the same situation a Scotland in 2014. They had the blessing of the UK parliament and were allowed to vote on it. The UK agreed beforehand to honor the outcome of the referendum. There would not have been war, and it is unlikely that there would have been civil war within Scotland.

If you do not have approval, you face the same situation as Catalonia in 2017, when the referendum they held was declared illegal. The Catalan people do not have independence, and in order to break free from Spain they would have to resort to violence. So far, the violence was very limited. This is an ongoing situation.

As far as popular support is concerned, you have Catalonia as example, where the spanish people in general do not want to let Catalonia go. If the catalan independence had vast support in the spanish populace, demonstrations all over spain could help the catalan people to gain approval for a legal independence referendum and force a change.

This happened in Czechoslovakia from 1989-1993. Widespread demonstrations, fueled by the violent suppression of an earlier demonstration with 9 people dead, lead to the fall of the communist government and a new government was installed. Splitting the country had popular support all over the country, allowing a peaceful transition.

So, in order to have a region split from a parent country, you have to figure out:

Why do they want independence? Is there a historical reason? Are there economical reasons? In case of the hypothetical partition of Belgium, historical and linguistic reasons are often cited, but the real reason for wanting to split is economical, the rich regions no longer wish to support the poor ones. The reasons for wanting independence are important because they directly drive who supports them. If a rich regions wants to split from a poor one, then usually the poor one doesn't want that, or if they do, they have to think they can be better off and improve their economy without being part of the larger country.

Who supports their independence? Which internal parties support the independence? Do they have popular support o both sides, if so, why (see above). Which external parties who could have a moderating effect or put pressure on the government support their independence?

What is their bargaining power? A stronger region can easily split from a weaker one simply by the threat of war. If the other side doesn't want independence, but the cost of war is too high, they might not want to do anything about it.

If you look at the pinnacle of "western civilization", the US, you can look at the various bids for Secession of California from the United States. After Trump was elected, secessionist movements in California flared up against after a long history of such movements.

Another problem within the US is the Kingdom of Hawaii. In 1993, the Apology resolution "acknowledges that the overthrow of the Kingdom of Hawaii occurred with the active participation of agents and citizens of the United States and further acknowledges that the Native Hawaiian people never directly relinquished to the United States their claims to their inherent sovereignty as a people over their national lands, either through the Kingdom of Hawaii or through a plebiscite or referendum.". it would be interesting to see what would happen if there was enough popular support within the Hawaiian populace to do something about it. the strategic importance of Hawaii is certainly big, but in times of social media, globalization and internet, can you really rule over a group of island where the people do not wish to be ruled by you and where you already recognized their claim to sovereignty?

Independence and Sovereignty aren't easy, but you can find enough historical examples even in the modern world where you can build upon claims of independence and take it from there. Put more pressure on California, have the US make decisions that are hugely unpopular in California, trash their economy and suddenly it becomes believable in a work of fiction that a few years down the drain the secessionist movement has gained enough support within California to do something about it. find an external actor who wants to help. In the case of the US, that is difficult, because which external actor would risk war with the US to ensure Californias independence? But there are smaller countries where claims of independence exist and bigger external actors might want to help gaining their independence, or where you can contrive a scenario where you have popular support for an amicable split.

Without war essentially means that the former owner of the area chooses to not go to war.

It might be simply incapable. Soviet Union, Czechoslovakia, and Yugoslavia de facto ceased to exist. Many countries became independent during the Russian Civil War or the unrest leading to it. This does not entirely make warfare impossible as the military forces and political machinery do not usually disintegrate with the state and may want to contest the dissolution. There was lots of warfare within Yugoslavia for example.

It might be prevented by external force. At the end of the World War I several new countries were formed from the parts of the losing powers.

I am not going to talk more about either of these options since they are predicated on some degree of conflict preceding the event even if it stops before the independence and avoids escalating to actual warfare.

So lets talk about reasons for genuinely choosing to let someone go.

It is the will of the people

Civil disobedience is a thing. Gandhi used it in India and in Finland similar tactics were used to resist Russification. In both cases external reasons eventually created the window of opportunity for independence but making the government aware that the people want independence is pretty much required for peaceful independence that is not forced by outside powers. Essentially if you can create a peaceful movement for independence capable of widespread and organized civil disobedience eventually the government will just give up.

In a democracy with a separate national parliament just having that parliament support independence with a large enough majority will work.

The two options above are very much not mutually exclusive. If your nation does not already have a separate parliament having one should be your goal before you start seriously trying to be independent. So civil disobedience to get a right to a parliament is a thing.

You can also get your parliament via politics within the political system of the larger nation. And you might be able to even skip the separate parliament if you already have solid representation. If the British government found itself dependent on the support of the Scottish National Party within the British Parliament, SNP wouldn't need to do anything in Scotland to get its views heard.

The time is right

Another important aspect is a discontinuity. Soviet Union felt no real need to enforce the ownership of Finland by the Russian Empire. Stalin (people's commissar for Nationalities at the time) was okay for Finland to become independent when he could use it to manage separatism in the Russia proper. And Lenin probably really thought right of secession was a thing. India gained independence because post WW2 the British Empire really didn't have the ability to keep them.

Sometimes a change of government might be enough. If the people want independence and the government has made waves opposing it, the opposition parties have probably spent years talking about how stupid forcing people to be part of a nation they do not actually support is. So when they win the election they will have a hard time continuing oppressing the liberty desire of the people.

Sometimes the independence is long process of a nation becoming ready for it. British Dominions just started handling more and more of their own affairs and became increasingly independent. Interestingly this was actually caused by the independence of the United States. Many felt that the bloodshed and violence was fundamentally caused by failure to properly deal with the political rights of the colonial citizens, so colonies with populations largely composed of European migrants that would expect to have political rights despite being far distant from London were given an improved status.

There is a political process for it

For the transition to happen peacefully without special circumstances it needs to be managed properly. It should result from political negotiation with a consensus on the result. This does not imply that both sides or even either side has to approve of the result. And the result certainly does not need to be popular. But you do need two sides that mutually agree they have the authority to negotiate and actually go thru the process.

Best (negative) example of this is probably Catalonia. Spain does not have a political system for negotiating a secession or even properly discussing it and it is a major issue for everyone concerned. There really isn't a good way for either the government or the separatists to deal with the issue.

This does imply that the separatists have a political organization that the government can accept as legitimate. Having a separate legal parliament makes this much easier but having leaders that are known to have popular support can be enough.

It also helps a lot if the political process for secession was defined in advance. If the process already exists both sides have the option of following it and not having to argue about it before they get to actual productive work.

Faking it

All of the above can be faked. Ability to convince the population that independence has great popular support is almost as good as actually having it. A political crisis and the window of opportunity can be manufactured. Sufficient amount of money in the right hands can grease the most difficult negotiation.

Have a war somewhere else, giving your new country an opportunity window to secede. Historical example, Slovenian seccesion from Yugoslavia after the Ten Days war. Yugoslav army had to withdraw in a hurry to face bigger threats, granting Slovenia de-facto independence after very limited fighting with no impact on economy or infrastructures, thus allowing something similar to your great start.

Counter-example from your question, Catalonia might not be able to secede without a war, but Basque Country might take advantage of the turmoil to set sails while Spanish army is up to its neck somewhere else.

As of today, there are some forces in the world that are becoming more powerful than most states. A combination of finance, natural resources, popular and international pressures could create the weather for a perfect storm.

Some concrete examples:

A. Former colonies are granted their independence

1. Due to international pressure and political turmoil, the US, UK, France, New Zealand and Spain commit themselves to grant independence to their current colonies 100 years from now.




2. Big corporations (subreptitiously) buy land in some colonial islands in the Pacific or the Caribbean and push for independence from the countries that control them.
   https://en.wikipedia.org/wiki/United_Nations_list_of_Non-Self-Governing_Territories#/media/File:UN-Non-Self-Governing_Territories.svg

B. Governance problems and democratic pressures

1. Canada is in bankrupt due to dwindling population and huge state expenses. Quebec votes for its independence. It receives a large support from the US and Europe due to probable oil and gas reserves. A weak Canadian government is forced to accept a debt reduction in exchange.




2. The Congress of California and its governor do not recognize the election of Donald Trump III for a third term and declare their independence. Oregon and other nearby states (could include Mexican states) follow their lead and form a new federation.

C. Financial district becomes a country.

China, Europe and the US agree for the need of an international financial district in order to maintain the balance of power in the world. Of course, the conditions that lead to such an agreement are yet to be seen.
The territory could be located somewhere in Europe (e.g. France and Germany agree to lose a small part of their territory in exchange for direct supervision and a privileged geographical position).
China is interested in having Europe as an ally against the emergent nuclear powers in Asia (Russia, India and Iran), and a debilitated US has to agree because its external debt with China has become unbearable.

One other example: Singapore leaving Malasia in 1965.
They did join in 1963 though, and they were small, poor and with different population and religion.