With the increasing requirements for efficient utilization of satellite resources, both non-orthogonal multiple access (NOMA) scheme and cognitive radio (CR) have been recognized as one of the promising solutions, particularly, for the enhancement of spectrum efficiency. This letter investigates the performance of NOMA-based integrated satellite-terrestrial relay network (ISTRN) in the presence of multiple primary users (PUs) under spectrum sharing environment. Specifically, we derive the closed-form expressions of outage probability (OP) and ergodic capacity (EC) of the considered system under the interference constraint imposed by multiple adjacent PUs. To get further insights, the asymptotic analysis for OP at high signal-to-noise ratios (SNRs) is also obtained. Numerical results are provided to verify our analysis and reveal the impacts of key parameters on system performance.