The winter North Atlantic Oscillation (NAO) is a major source of seasonal climate variability across the Euro-Atlantic region, and part of its predictability arises from persistent North Atlantic sea-surface temperature (SST) anomalies. Whether this SST–NAO relationship remains stationary under anthropogenic forcing is uncertain. Here we investigate the evolution of North Atlantic SST–NAO predictability using the 40-member CANARI large ensemble under SSP3-7.0 forcing together with a hierarchy of physically constrained statistical and machine-learning models. We find that the internal component of the SST–NAO teleconnection retains a largely stable spatial structure throughout the 21st century, although the subpolar North Atlantic contribution weakens. In contrast, the externally forced SST–NAO relationship changes substantially as the North Atlantic warming pattern evolves. A three-term stationarity budget shows that forecast-skill degradation in the early 21st century is dominated by changes in the forced mean state rather than by increased internal variability. By the late century, the forced SST–NAO regression reverses sign as differential warming between the tropical and subpolar North Atlantic strengthens. A decomposition of predictability sources indicates a transition from historically interaction-driven predictability, in which forced and internal SST components jointly contribute to NAO skill, toward a regime in which the forced SST component becomes increasingly important. All model configurations exhibit a comparable decline in skill under SSP3-7.0, suggesting that the degradation arises primarily from changes in the climate background state rather than from the choice of statistical architecture. ERA5 reanalysis data show an emerging positive shift in the recent winter NAO relative to the historical baseline, consistent with the early stages of the simulated transition. Together, these results suggest that future seasonal prediction systems may require periodic recalibration as the North Atlantic mean state evolves under continued anthropogenic forcing.