Most Multi-view Clustering approaches assume that all views are available for clustering. However, this assumption is often unrealistic as views are incrementally accumulated over time, leading to a need for continual multi-view clustering (CMVC) methods. Current approaches to CMVC leverage late fusion-based approaches, where a new model is typically learned individually for each view to obtain the corresponding partition matrix, and then used to update a consensus matrix via a moving average. These approaches are prone to view-specific noise and struggle to adapt to large gaps between different views. To address these shortcomings, we reconsider CMVC from the perspective of domain adaption and propose AdaptCMVC, which learns how to incrementally accumulate knowledge of new views as they become available and prevents catastrophic forgetting. Specifically, a self-training framework is introduced to extend the model to new views, particularly designed to be robust to view-specific noise. Further, to combat catastrophic forgetting, a structure alignment mechanism is proposed to enable the model to explore the global group structure across multiple views. Experiments on several multi-view benchmarks demonstrate the effectiveness of our proposed method on the CMVC task. Our code is released in the supplementary materials.