Most earth system models (ESMs) neglect climate feedbacks arising from carbon release from thawing permafrost, especially from thawing of subsea permafrost (SSPF). To assess the fate of SSPF in the next 1000 years, we implemented SSPF into JSBACH, the land component of the Max Planck Institute Earth System Model (MPI-ESM). This is the first implementation of SSPF processes in an ESM component. We investigate three extended scenarios from the 6th phase of the Coupled Model Intercomparison Project (CMIP6). In the 21st century only small differences are found among the scenarios, but in the upper-end emission scenario SSP5-8.5 (shared socio-economic pathway), especially in the 22nd century, SSPF ice melting is more than 15 times faster than in the pre-industrial period. In this scenario about 35ĝ% of total SSPF volume and 34ĝ% of SSPF area are lost by the year 3000 due to climatic changes. In the more moderate scenarios, the melting rate maximally exceeds that of pre-industrial times by a factor of 4, and the climate change induced SSPF loss (volume and area) by the year 3000 does not exceed 14ĝ%. Our results suggest that the rate of melting of SSPF ice is related to the length of the local open-water season and thus that the easily observable sea ice concentration may be used as a proxy for the change in SSPF.