Multi-view clustering is a prominent area of interest in machine learning and data mining. However, most existing methods are confined to static multi-view data, posing challenges for achieving multi-view information fusion and clustering in a dynamic streaming context. We propose a multi-view streaming clustering with incremental anchor learning, which effectively partitions continuous chunks of multi-view data into meaningful clusters. Initially, a shared subspace representation is derived to reveal the intrinsic structure hidden across views, which is adapted to the evolving data distribution through incremental learning of anchors. Furthermore, the shared subspace representation, anchors, and clustering assignments are learned simultaneously in a unified framework, where their interactive negotiation avoids the suboptimal solution problem and significantly enhances overall clustering performance. Finally, extensive experiments on several real-world datasets demonstrate that the proposed method achieves superior multi-view clustering performance and efficiency in a streaming context.