Discovering new intents is crucial for many systems to adapt to evolving users’ needs, making it inherently a continual process. However, most related studies have not explored such continual learning scenarios for new intent discovery. To bridge this research gap, we formalize the Continual Open-Stream Intent Discovery (COSID) task, which requires simultaneous detection of historical intents and discovery of new ones from hybrid streaming data. Our central contribution is a configurable open-stream dataset construction protocol that transforms a static intent dataset into a stream of temporally partitioned datasets, as well as a set of evaluation metrics for the COSID task. We further propose the Continual Intent Discovery Agent (CIDA) for the task, a memory-augmented agent that screens the incoming stream, clusters new-intents’ samples, and employs an LLM for intent abstraction and memory expansion. Experiments on the ClincCL and BankCL data streams constructed according to our protocol validate both the protocol expressiveness and agent superiority over existing baselines.