This paper studies the problem of fair clustering on heterogeneous information networks (HINs) by considering constraints on structural and sensitive attributes. We propose a Prerequisite-driven Fair Clustering (PDFC ) algorithm to solve this problem. Specifically, we define the structural constraint on the connection among nodes in HINs by combining meta-paths and prerequisite meta-paths and introduce Fairlets as the balance constraint. Under two constraints, we learn node embeddings based on graph models and perform theCholesky decomposition to obtain their orthogonal embeddings. We fuse node embeddings under constraints, define the loss function of PDFC, and perform k-means to achieve clustering. In addition, we design an update strategy of the adjacency matrix to achieve dynamic PDFC over time. Compared with several fair clustering algorithms on three real-world datasets, our experimental results verify the effectiveness and efficiency of PDFC.