Intent detection aims to identify user intents from natural language inputs, where supervised methods rely heavily on labeled in-domain (IND) data and struggle with out-of-domain (OOD) intents, limiting their practical applicability. Generalized Intent Discovery (GID) addresses this by leveraging unlabeled OOD data to discover new intents without additional annotation. However, existing methods focus solely on clustering unsupervised data while neglecting domain adaptation. Therefore, we propose a consistency-driven prototype-prompting framework for GID from the perspective of integrating old and new knowledge, which includes a prototype-prompting framework for transferring old knowledge from external sources, and a hierarchical consistency constraint for learning new knowledge from target domains. We conducted extensive experiments and the results show that our method significantly outperforms all baseline methods, achieving state-of-the-art results, which strongly demonstrates the effectiveness and generalization of our methods. Our source code is publicly available at https://github.com/smileix/cpp.