Despite many advances in self-adaptive systems (SAS) research, the community has only recently begun exploring the evolution of SASs. We consider an evolution to be a necessary change of the SAS outside of its self-adaptation capabilities, e.g., to respond to unforeseen changes. In this work, we study the assurance of evolving SASs. Dynamic assurance cases (ACs) have been proposed as a means to certify a system’s safety and reliability under uncertainty. However, when the SAS evolves, developers require guidance about which parts of a dynamic AC can be repurposed and which costs may be introduced in re-assuring the evolved SAS. Towards this goal, we propose ReASSURE, a framework which provides a structured approach for reusing assurance evidence for evolving SASs. Building on existing techniques for dynamic AC development, compositional assurance, and product line engineering, ReASSURE aims to maximize reuse, minimize the cost, and quantify the effort of assuring evolving SASs.