Advancements in artificial intelligence are rapidly increasing. The new-generation large language models, such as ChatGPT and GPT-4, bear the potential to transform educational approaches, such as peer-feedback. To investigate peer-feedback at the intersection of natural language processing (NLP) and educational research, this paper suggests a cross-disciplinary framework that aims to facilitate the development of NLP-based adaptive measures for supporting peer-feedback processes in digital learning environments. To conceptualize this process, we introduce a peer-feedback process model, which describes learners' activities and textual products. Further, we introduce a terminological and procedural scheme that facilitates systematically deriving measures to foster the peer-feedback process and how NLP may enhance the adaptivity of such learning support. Building on prior research on education and NLP, we apply this scheme to all learner activities of the peer-feedback process model to exemplify a range of NLP-based adaptive support measures. We also discuss the current challenges and suggest directions for future cross-disciplinary research on the effectiveness and other dimensions of NLP-based adaptive support for peer-feedback. Building on our suggested framework, future research and collaborations at the intersection of education and NLP can innovate peer-feedback in digital learning environments.