AI models are rapidly becoming embedded in all aspects of nuclear energy research and work but the safety, security, and safeguards consequences of this embedding are not well understood. In this paper, we call for the creation of an anticipatory system of governance for AI in the nuclear sector as well as the creation of a global AI observatory as a means for operationalizing anticipatory governance. The paper explores the contours of the nuclear AI observatory and an anticipatory system of governance by drawing on work in science and technology studies, public policy, and foresight studies.