The ability of forests to continuously provide ecosystem services (ES) is threatened by rapid changes in climate and disturbance regimes. Consequently, these changes present a considerable challenge for forest managers. Management of forests often focuses on maximizing the level of ES provisioning over extended time frames (i.e., rotation periods of more than 100 yr). However, temporal stability is also crucial for many ES, for example, in the context of a steady provisioning of resources to the industry, or the protection of human infrastructure against natural hazards. How temporal stability and the level of ES provisioning are related is of increasing interest, particularly since changing climate and disturbance regimes amplify temporal variability in forest ecosystems. In this simulation study, we investigated whether forest management can simultaneously achieve high levels and temporal stability of ES provisioning. Specifically, we quantified (1) trade-offs between ES stability and level of ES provisioning, and (2) the effect of tree species diversity on ES stability. Simulating a wide range of future climate scenarios and management strategies, we found a negative relationship between temporal stability and level of ES provisioning for timber production, carbon cycling, and site protection in a landscape in the Austrian Alps. Tree species diversity had a predominantly positive effect on ES stability. We conclude that attempts to maximize the level of ES provisioning may increase its temporal variability, and thus threaten the continuity of ES supply. Consequently, considerations of stability need to be more explicitly included in forest management planning under increasingly variable future conditions.