Global warming may modify submesoscale activity in the ocean through changes in the mixed layer depth and lateral buoyancy gradients. As a case study we consider a region in the Northeast Atlantic under present and future climate conditions, using a time-slice method and global and nested regional ocean models. The high resolution regional model reproduces the strong seasonal cycle in submesoscale activity observed under present-day conditions. In the future, with a reduction in the mixed layer depth, there is a substantial reduction in submesoscale activity and an associated decrease in kinetic energy at the mesoscale. The vertical buoyancy flux induced by submesoscale activity is reduced by a factor of 2. When submesoscale activity is suppressed, by increasing the parameterized lateral mixing in the model, the climate change induces a larger reduction in winter mixed layer depths while there is less of a change in kinetic energy at the mesoscale. A scaling for the vertical buoyancy flux proposed by Fox-Kemper et.\ al.\, based on the properties of mixed layer instability (MLI), is found to capture much of the seasonal and future changes to the flux in terms of regional averages as well as the spatial structure, although it over predicts the reduction in the flux in the winter months. The vertical buoyancy flux when the mixed layer is relatively shallow is significantly greater than that given by the scaling based on MLI, suggesting during these times other processes (besides MLI) may dominate submesoscale buoyancy fluxes.