Achieving food security in the face of climate change is a major challenge for humanity in the 21st century but comprehensive analyses of climate change impacts, including global market feedbacks are still lacking. In the context of uneven impacts of climate change across regions interconnected through trade, climate change impact and adaptation policies in one region need to be assessed in a global framework. Focusing on four Eastern Asian countries and using a global integrated modeling framework we show that i) once imports are considered, the overall climate change impact on the amount of food available could be of opposite sign to the direct domestic impacts and ii) production and trade adjustments following price signals could reduce the spread of climate change impacts on food availability. We then investigated how pressure on the food system in Eastern Asia could be mitigated by a consumer support policy. We found that the costs of adaptation policies to 2050 varied greatly across climate projections. The costs of consumer support policies would also be lower if only implemented in one region but market price leakage could exacerbate pressure on food systems in other regions. We conclude that climate adaptation should no longer be viewed only as a geographically isolated local problem.