The Arctic Ocean is an early warning system for indicators and effects of climate change. We use a novel combination of experimental and time-series data on effects of ocean warming and acidification on the commercially important Northeast Arctic cod (Gadus morhua) to incorporate these physiological processes into the recruitment model of the fish population. By running an ecological-economic optimization model, we investigate how the interaction of ocean warming, acidification and fishing pressure affects the sustainability of the fishery in terms of ecological, economic, social and consumer-related indicators, ranging from present day conditions up to future climate change scenarios. We find that near-term climate change will benefit the fishery, but under likely future warming and acidification this large fishery is at risk of collapse by the end of the century, even with the best adaptation effort in terms of reduced fishing pressure.