The rising complexity and interconnectedness of contemporary systems engineering solutions have spurred the development of Systems-of-Systems (SoS). Within a SoS, we find interconnected constituent systems (CSs), each possessing individual capabilities and managerial autonomy. For effective management of a SoS, a dedicated orchestration mechanism is crucial. However, currently, there is a lack of a well-defined internal structure or an understanding of roles and interactions between sub-parts of the Orchestrator. This paper proposes a framework for SoS orchestration, identifying distinct actors and their functional roles for an effective SoS operation. Our framework consists of two main groups: SoS Governors (handling legal and financial aspects) and the Orchestrator (responsible for the overall SoS operation). Key actors within the Orchestrator are identified and described, including the Goal Transformer, Registrar, Composer, Executor, Cartographer, Data Curator, and Translator. The paper concludes by discussing the dynamic collaboration between orchestration actors and the significance of clearly defining these roles for complex SoS management. This study offers a foundation for future research and practice in SoS orchestration, potentially enhancing these complex systems’ resilience, effectiveness, and overall management.