Functional traits offer a potential avenue to generalize and forecast the impacts of changing competition on plant communities, including changing outcomes of competition among species that currently interact (current competition) or that will interact in the future following range shifts (novel competition). However, it remains unclear how well traits explain variation in the outcomes of current and novel competition as well as the underlying processes determining coexistence or competitive exclusion, under changing climate. Here, we interacted pairs of high and low-elevation species in three sites across an elevation gradient in the Swiss Alps. For each species pair, we quantified the population-level outcomes of competition (invasion growth rates), relative fitness differences, and niche overlap and related these to 15 functional traits that were measured in each site. Most traits were significantly associated with invasion growth rates at the low elevation, where species had greater relative fitness differences, but these associations were much weaker towards higher elevations. This appears to be because traits, particularly those associated with light competition, captured species' relative fitness differences at lower elevations, but not at the high elevation site, highlighting that the predictive ability of traits can depend on environmental context. The amplified relative fitness differences towards lower elevations suggest that climate warming may increase the likelihood of competitive exclusion. In addition, novel competitors tended to show greater niche overlap than current competitors, leading to stronger overall competitive effects. However, in general, trait differences predicted competitive outcomes of novel and current competitors similarly well, suggesting that traits can predict interactions between species that do not yet interact. Our study reinforces the importance of considering changing interactions for predicting species responses to climate change and provides experimental evidence supporting the usefulness of functional trait differences in forecasting the impacts of future plant interactions under changing climate.