In this paper, we study the case of an overlay cognitive radio network where the primary user (PU) leases spectral resources to the secondary user (SU) in exchange for cooperation. Considering, a two-phase leasing process, a novel time allocation mechanism is analyzed and proposed. In particular, we focus on the maximization of PU’s effective capacity while guaranteeing a minimum effective capacity value for the SU as well. The optimal time allocation for the secondary access is calculated using the theory of convex optimization. The numerical results demonstrate the performance of the proposed mechanism for various network parameters and some interesting conclusions are drawn. Keywordsoverlay cognitive radio, time allocation, statistical quality-of-service (QoS) provisioning, effective capacity.