Multi-view clustering thrives in applications where views are collected in advance by extracting consistent and complementary information among views. However, it overlooks scenarios where data views are collected sequentially, i.e., real-time data. Due to privacy issues or memory burden, previous views are not available with time in these situations. Some methods are proposed to handle it but are trapped in a stability-plasticity dilemma. In specific, these methods undergo a catastrophic forgetting of prior knowledge when a new view is attained. Such a catastrophic forgetting problem (CFP) would cause the consistent and complementary information hard to get and affect the clustering performance. To tackle this, we propose a novel method termed Contrastive Continual Multi-view Clustering with Filtered Structural Fusion (CCMVC-FSF). Precisely, considering that data correlations play a vital role in clustering and prior knowledge ought to guide the clustering process of a new view, we develop a data buffer with fixed size to store filtered structural information and utilize it to guide the generation of a robust partition matrix via contrastive learning. Furthermore, we theoretically connect CCMVC-FSF with semi-supervised learning and knowledge distillation. Extensive experiments exhibit the excellence of the proposed method.