Non-orthogonal multiple access (NOMA) along with cognitive radio (CR) have been recently configured as potential solutions to fulfill the extraordinary demands of the fifth generation (5G) and beyond (B5G) networks and support the Internet of Thing (IoT) applications. Multiple users can be served within the same orthogonal domains in NOMA via power-domain multiplexing, whilst CR allows secondary users (SUs) to access the licensed spectrum frequency. This work investigates the possibility of combining orthogonal frequency division multiple access (OFDMA), NOMA, and CR, referred to as hybrid OFDMA-NOMA CR network. With this hybrid technology, the licensed frequency is divided into several channels, such as a group SUs is served in each channel based on NOMA technology. In particular, a rate-maximization framework is developed, at which user pairing at each channel, power allocations for each user, and secondary users activities are jointly considered to maximize the sum-rate of the hybrid OFDMA-NOMA CR network, while maintaining a set of relevant NOMA and CR constraints. The developed sum-rate maximization framework is NP-hard problem, and cannot be solved through classical approaches. Accordingly, we propose a two-stage approach; in the first stage, we propose a novel user pairing algorithm. With this, an iterative algorithm based on the sequential convex approximation is proposed to evaluate the solution of the non-convex rate-maximization problem, in the second stage. Results show that our proposed algorithm outperforms the existing schemes, and CR network features play a major role in deciding the overall network’s performance.