Due to the dynamics of spectrum and ad-hoc networking, traditional clustering protocols have the issue of high clustering frequency and large communication overhead. To address the issue, this paper for the first time proposes a network stability-aware clustering (NSAC) protocol for cognitive radio sensor networks. In NSAC protocol, each node searches the maximum edge biclique based on its neighbors and available channels. The weight of one node is calculated based on the remaining energy, the numbers of nodes and available common control channels in its maximum edge biclique. The node with the largest weight in the neighborhood will be selected as the cluster head, and the rest of nodes in the neighborhood join the cluster as members. As energy consumption and spectrum dynamics are sufficiently considered in the clustering process, network lifetime and network stability are significantly enhanced. Extensive simulations show that the proposed NSAC protocol markedly outperforms existing works in the aspects of network lifetime and network stability.