This paper presents the governance framework developed for FRIDGE (Federated Research Infrastructure by Data Governance Extension), a model that extends Trusted Research Environment (TRE) governance boundaries to large-scale external AI supercomputing infrastructure. FRIDGE provisions an ephemeral satellite TRE as a secure enclave on external compute, bringing it under the control of an existing TRE and its governance framework, removing the need to renegotiate data sharing agreements with hosting providers or data owners. Developed in collaboration with the technical teams at two UK AI Research Resource (AIRR) sites, the Bristol Centre for Supercomputing (BriCS, hosting Isambard-AI) and the University of Cambridge Research Computing Service (hosting Dawn), the paper sets out a Shared Responsibility Model delineating obligations across the FRIDGE Hosting Organisation, TRE Operator Organisation, and Resource Allocator (mapped to the Five Safes framework); a Roles Catalogue covering organisational, governance, technical, and researcher roles across the full operational lifecycle; and lifecycle sequence diagrams documenting cross-boundary handoff points from project initialisation through provisioning, active research use, teardown, and termination. The outputs align with the emerging SATRE 2.0 Federation pillar, constituting an early real-world implementation of federation requirements 5.1.01, 5.1.02, and 5.5.01. The paper also identifies key gaps, most notably the absence of a TRE-aware access call pathway within the current AIRR process, and policy/agreement gaps at AIRR sites, and sets out a roadmap for moving FRIDGE from validated prototype to a production-ready service for sensitive data research.