Implementing a knowledge system: Lessons from the global stewardship of climate services

•Identify the activities of a global climate service knowledge system (KS).•Analyze the Global Framework of Climate Services as a KS.•Key activities include shaping vision, building capacity, and creating connections.•KS tensions relate to its purpose and who has influence in the KS.•Strategies for KS stewardship are theorizing, legitimizing, and managing knowledge.