CMIP5 models have been shown to exhibit rapid cooling events in their projections of the North Atlantic subpolar gyre. Here, we analyze the CMIP6 archive, searching for such rapid cooling events in the new generation of models. Four models out of 35 exhibit such instabilities. The climatic impacts of these events are large on decadal timescales, with a substantial effect on surface temperature over Europe, precipitation pattern in the tropics—most notably the Sahel and Amazon regions—and a possible impact on the mean atmospheric circulation. The mechanisms leading to these events are related to the collapse of deep convection in the subpolar gyre, modifying profoundly the oceanic circulation. Analysis of stratification in the subpolar gyre as compared with observations highlights that the biases of the models explain relatively well the spread in their projections of surface temperature trends: models showing the smallest stratification biases over the recent period also show the weakest warming trends. The models exhibiting abrupt cooling rank among the 11 best models for this stratification indicator, leading to a risk of encountering an abrupt cooling event of up to 36.4%, slightly lower than the 45.5% estimated in CMIP5 models.