The climate sensitivity of carbon (C) cycling in Arctic terrestrial ecosystems is a major unknown in the Earth system. There is a lack of knowledge about the mechanisms that drive the interactions between photosynthesis, respiration and changes in C stocks across full annual cycles in Arctic tundra. We use a calibrated and validated model (SPA) to estimate net ecosystem exchange (NEE), gross primary production (GPP), ecosystem respiration (Reco) and internal C processing across eight full years. SPA's carbon flux estimates are validated with observational data obtained from the Greenland Ecosystem Monitoring programme in West Greenland tundra. Overall, the model explained 73%, 73% and 50% of the variance in NEE, GPP and Reco respectively and 85% of the plant greenness variation. Flux data highlighted the insensitivity of growing season NEE to inter‐annual meteorological variability, due to compensatory responses of photosynthesis and ecosystem respiration. In this modelling study, we show that this NEE buffering is the case also for full annual cycles. We show through a sensitivity analysis that plant traits related to nitrogen are likely key determinants in the compensatory response, through simulated links to photosynthesis and plant respiration. Interestingly, we found a similar temperature sensitivity of the trait‐flux couplings for GPP and Reco, suggesting that plant traits drive the stabilization of NEE. Further, model analysis indicated that wintertime periods decreased the C sink by 60%, mostly driven by litter heterotrophic respiration. This result emphasizes the importance of wintertime periods and allows a more comprehensive understanding of full annual C dynamics.