<p>Artificial intelligence systems often face the challenge of inconsistency between the source and target domains in real-world. How to continuously discover novel categories in open-world target environments remains a challenging problem. In this paper, we address a more realistic and challenging task: Continual Novel Class Discovery under Domain Shift (CNCD-DS). Our goal is to continuously discover and learn novel classes in an unlabeled, domain-shifted dataset that contains a mixture of known and novel classes. Existing novel class discovery methods frequently ignore domain shift, a critical oversight that leads to performance collapse when distributions change. To this end, we propose a discovery and enhancement method to improve model discriminative capability. Our solution is a novel progressive method consisting of a discovery phase and an enhancement phase. The discovery phase employs an entropy-based selection mechanism to identify high-confidence samples. The enhancement phase employs prototype-based supervision to learn diverse features from high-confidence samples and then optimizing the representations of each class using all available data. This process is then repeated iteratively for new incoming tasks. Extensive experiments demonstrate that our method outperforms existing baseline methods under various conditions.</p>