The relative arrival time of species often affects species interactions within a community, contributing to priority effects. Recent studies on phenological shifts under climate change have generated renewed interest on priority effects, but their role in shaping long-term dynamics of seasonal communities is poorly resolved. Here we use a general stage-structure competition model to determine how different types of priority effects influence long-term coexistence of species in seasonal systems. We show that while shifts in mean and variance of relative arrival time can alter persistence and coexistence conditions of species, these effects depend on season length and type of priority effect. In "slow" systems with one or a few cohorts per season, changes in mean and seasonal variation of relative arrival time strongly altered species persistence through trait-mediated priority effects. In contrast, competition outcome in "fast" systems is largely determined by numeric priority effects due to interaction between many overlapping generations. These results suggest that empirically observed priority effects may arise from fundamentally different mechanisms, and that fast-generating systems may be less impacted by seasonal variation in phenology. Our model provides important insight into how natural communities respond to increasing variation in phenology over seasons under climate change.