Cognitive radio (CR) network is the effective technique for the optimum utilization of the spectrum. The hybrid cognitive network (HCN) has been implemented to increase the utilization of the spectrum, by using both (overlay/underlay) modes of spectrum sharing. In overlay mode, cognitive radio (CR) opportunistically uses the spectrum, whereas in underlay mode, the CR uses the spectrum simultaneously with primary user (PU) with transmit power limitation. The HCN tries to use advantages of both modes of spectrum sharing. Its performance is based on the accuracy of the method used to find the PU status. Hence, in this paper, "clustering-based spectrum access scheme selection and optimal relay link selection for hybrid overlay/underlay cognitive radio networks" have been proposed to improve the performance of the hybrid cognitive radio network. In this proposed method, the scheme selection is done in two levels. In the first level, spectrum sharing scheme is selected based on the cluster in which the SU is present, and in the second level, scheme is selected based on the PU status. The cluster-based cooperative spectrum sensing method has been used to find the status of the PU. Compared with cooperative spectrum sensing, a cluster-based cooperative spectrum sensing has a huge effect on sensing accuracy. While the underlay scheme is used by SU, best relay link has been selected by using particle swarm optimization technique. Thus, the best scheme selection and relay selection improve the performance of hybrid cognitive radio network. The simulation result shows that the proposed method improves the throughput of the HCN.