This report examines the evolving role of the United Nations and International Geneva in global AI governance, focusing on institutional pathways, normative frameworks, and policy implications beyond 2025. Using desk research, institutional mapping, and expert interviews, it finds that governance remains fragmented and largely normative, with the UN acting more as a convenor than a regulator due to limited technical capacity, political coherence, and coordination across mandates. Divergent regional models, risks of private-sector dominance, and underrepresentation of the Global South further complicate harmonisation. Despite these challenges, opportunities exist to strengthen AI governance through soft law tools, co-governance platforms, inclusive rights-based approaches, and anticipatory mechanisms such as foresight and regulatory sandboxes. The report recommends flexible UN coordination, technical capacity building, participatory norm creation, scalable governance tools, and adaptive regulation, concluding that effective AI governance will require iterative, inclusive, and distributed efforts rather than a single binding framework.