The emergence of Generative Artificial Intelligence (GenAI) has reshaped the interpreting practice and imposed new demands on interpreter competence. Consequently, interpreter training in higher education requires systematic reform to meet the challenge. This paper first reviews the conceptual origins and core components of interpreter competence. On this basis, it identifies three key elements for upgraded interpreter competence: improved interpreting skills, expanded technological capabilities, and updated professional qualities. The paper then discusses how interpreter training in higher education can be reformed in light of the upgraded competence. It proposed the enrichment of curriculum design and teaching content, and the optimization of training progression and arrangements so as to reflect the complex and dynamic nature of interpreter competence. At the same time, greater emphasis should be placed on higher-order thinking abilities. This study aims to provide insights for interpreter training and the sustainable professional development of interpreters in the GenAI era.