Non-orthogonal multiple access (NOMA) and cooperative spectrum sharing (CSS) are integrated into this work to enhance both spectrum efficiency and utilization. A clustering-based overlay spectrum sharing is proposed by exploiting NOMA in coordinated direct and relay transmission (CDRT) (termed as CSS-NOMA-CDRT). In CSS-NOMA-CDRT, a primary strong NOMA user is directly served by the primary transmitter, whereas a primary NOMA weak user needs the assistance of a relay to communicate with the primary transmitter within a cluster. Instead of using a dedicated relay, a secondary transmitter acts as a relay to forward the primary symbol to NOMA weak user and the secondary transmitter transmits own symbol to its receiver at the same time. The performance of the proposed CSS-NOMA-CDRT is evaluated with closed-form solutions, in terms of ergodic sum capacity and outage probability. Through the analytical and Monte Carlo simulation results, it is demonstrated that CSS-NOMA-CDRT can obtain remarkable capacity gain as compared to the conventional NOMA-based CDRT.