In this paper, we investigate the resource allocation algorithm design for cooperative cognitive relaying multicarrier non-orthogonal multiple access (MC-NOMA) systems. In particular, the secondary base station serves multiple secondary users and simultaneously acts as a relay assisting the information transmission in the primary network. The resource allocation aims to maximize the weighted system throughput by jointly optimizing the power and subcarrier allocation for both the primary and the secondary networks while satisfying the quality-of-service requirements of the primary users. The algorithm design is formulated as a mixed combinatorial non-convex optimization problem. We apply monotonic optimization theory to solve the problem leading to an optimal resource allocation policy. Besides, we develop a low-complexity scheme to find a suboptimal solution. Our simulation results reveal that the performance of the proposed suboptimal algorithm closely approaches that of the optimal one. Besides, the combination of MC-NOMA and cognitive relaying improves the system throughput considerably compared to conventional multicarrier cognitive relaying systems.