This theoretical review examines the leadership capabilities academic libraries require as artificial intelligence develops from generative assistance toward agentic systems that can plan, retrieve information, use tools, and coordinate multi-step knowledge workflows. It addresses a gap in social-science and library scholarship: AI adoption, AI literacy, and responsible-AI governance are often discussed separately, with limited integration into a leadership-capability framework for future-ready academic libraries. Using an integrative conceptual synthesis of literature on academic libraries, AI literacy, professional learning, responsible-AI governance, and agentic systems, the article develops a capability-led framework that links strategic leadership, ethical governance, staff learning, human-AI work design, and continuous assurance. The contribution is to show how staff learning functions not only as professional development but also as a governance mechanism that translates responsible-AI principles into everyday scholarly-service practice. The framework offers a basis for empirical testing and for practical decision-making in AI-enabled academic library services.