Community search on dynamic heterogeneous information networks (DAHIN) aims to identify stable and cohesive communities by capturing temporal correlations across snapshots, benefiting applications like personalized recommendations and team formation. Existing methods rely on full retraining, making them inefficient for handling continuous updates with diverse node/edge types and dynamic attributes, leading to weak adaptability to incremental data and low knowledge transfer efficiency. To address these issues, we propose Incremental Community Search in Dynamic Attributed Heterogeneous Information Networks(DAHIN-INCE), an incremental learning framework leveraging snapshot subset generation and knowledge distillation to generate snapshot subset for training based on historical information and new data, and integrates past and new knowledge through knowledge distillation to enhance learning efficiency. Experiments on four real-world datasets, including full retraining comparisons and ablation studies, validate the effectiveness of our approach.