Ocean eddies play a critical role in climate and marine life. In the rapidly warming Arctic, little is known about how ocean eddy activity will change because existing climate models cannot resolve Arctic Ocean mesoscale eddies. Here, by employing a next-generation global sea ice–ocean model with kilometre-scale horizontal resolution in the Arctic, we find a surge of eddy kinetic energy in the upper Arctic Ocean, tripling on average in a four-degree-warmer world. The driving mechanism behind this surge is an increase in eddy generation due to enhanced baroclinic instability. Despite the decline of sea ice, eddy killing (a process in which eddies are dampened by sea ice and winds) will not weaken in its annual mean effect in the considered warming scenario. Our study suggests the importance of adequately representing Arctic eddy activity in climate models for understanding the impacts of its increase on climate and ecosystems.