The release of carbon from thawing permafrost soils could amplify future climate warming. However, this feedback is highly uncertain because most Earth system models (ESM) do not represent permafrost carbon. We have improved the Institut Pierre-Simon Laplace ESM by including permafrost physical, carbon and nitrogen processes to better represent Arctic ecosystems. The model more accurately represents past and present permafrost physics and biogeochemistry, paving the way for future projections.