MOTIVATION: Accurate prediction of protein function is essential for elucidating molecular mechanisms and advancing biological and therapeutic discovery. Yet experimental annotation lags far behind the rapid growth of protein sequence data. Computational approaches address this gap by associating proteins with Gene Ontology (GO) terms, which encode functional knowledge through hierarchical relations and textual definitions. However, existing models often emphasize one modality over the other, limiting their ability to generalize, particularly to unseen or newly introduced GO terms that frequently arise as the ontology evolves, and making the previously trained models outdated. RESULTS: We present STAR-GO, a Transformer-based framework that jointly models the semantic and structural characteristics of GO terms to enhance zero-shot protein function prediction. STAR-GO integrates textual definitions with ontology graph structure to learn unified GO representations, which are processed in hierarchical order to propagate information from general to specific terms. These representations are then aligned with protein sequence embeddings to capture sequence-function relationships. STAR-GO achieves state-of-the-art performance and superior zero-shot generalization, demonstrating the utility of integrating semantics and structure for robust and adaptable protein function prediction. AVAILABILITY: Code and pre-trained models are available at https://github.com/boun-tabi-lifelu/stargo, https://doi.org/10.5281/zenodo.18643082.