Abstract The North Atlantic Oscillation (NAO) plays a leading role in modulating wintertime climate over the North Atlantic and the surrounding continents of Europe and North America. Here we show that the observed evolution of the NAO displays larger multi-decadal variability than that simulated by nearly all CMIP6 models. To investigate the role of the NAO as a pacemaker of multi-decadal climate variability, we analyse simulations that are constrained to follow the observed NAO. We use a particle filter data-assimilation technique that sub-selects members that follow the observed NAO among an ensemble of simulations, as well as the El Niño Southern Oscillation and Southern Annular Mode in a global climate model, without the use of nudging terms. Since the climate model also contains external forcings, these simulations can be used to compare the simulated forced response to the effect of the three assimilated modes. Concentrating on the 28 year periods of strongest observed NAO trends, we show that NAO variability leads to large multi-decadal trends in temperature and precipitation over Northern Hemisphere land as well as in sea-ice concentration. The Atlantic subpolar gyre region is particularly strongly influenced by the NAO, with links found to both concurrent atmospheric variability and to the Atlantic Meridional Overturning Circulation (AMOC). Care thus needs to be taken to account for impacts of the NAO when using sea surface temperature in this region as a proxy for AMOC strength over decadal to multi-decadal time-scales. Our results have important implications for climate analyses of the North Atlantic region and highlight the need for further work to understand the causes of multi-decadal NAO variability.