International relations is such a complex issue that no single challenge stands out as more important than others. Instead, there are several different related issues that are likely to be challenging.
The first is income inequality between nations, something that often fuels extensive migration. From the point of view of poor nations, for whom colonialism was a contributory factor to poverty, the issue is seen as income inequality, while wealthy nations see migration as an issue. In reality, though, these are the same problem, as disparities in wealth are a major driver of migration.
The ongoing effects of global climate change may exacerbate income inequality and migration, especially as many nations near the equator and island nations are most likely to be affected adversely by climate change and have the least resources to cope with it. On the other hand, wealthy nations, especially in the global north, make a disproportionate contribution to climate change.
Dealing with the tensions caused by these issues will likely be a key issue in international relations, as many of these problems can only be solved globally through multilateral institutions. And yet, economic upheavals tend to result in nativism and populism, which are major obstacles to global cooperation and cause nations to turn away from global institutions towards isolationism.