Hybridization is increasingly recognized as a potent evolutionary force. Though additive genetic variation and novel combinations of parental genes theoretically increase the potential for hybrid species to adapt, few empirical studies have investigated the adaptive potential within a hybrid species. Here, we investigate factors promoting phenotypic divergence using genomically diverged island populations of the homoploid hybrid Italian sparrow Passer italiae from Crete, Corsica, and Sicily. We address whether genomic contingencies, adaptation to climate or diet best explain divergence in beak morphology. Populations vary significantly in beak morphology, both between and within islands of origin. Temperature seasonality best explains population divergence in beak size. Interestingly, beak shape along all significant dimensions of variation was best explained by annual precipitation, genomic composition and their interaction, suggesting a role for contingencies. Moreover, beak shape similarity to a parent species correlates with proportion of the genome inherited from that species, consistent with the presence of contingencies. In conclusion, adaptation to local conditions and genomic contingencies arising from putatively independent hybridization events jointly explain beak morphology in the Italian sparrow. Hence, hybridization may induce contingencies and restrict evolution in certain directions dependent on the genetic background.