In the past decade, cognitive radio-inspired non-orthogonal multiple access (CR-NOMA) have gained prominence as a technology aimed at enhancing spectrum efficiency via dynamic spectrum access methods. In the wake of the shifting research focus beyond the five-generation (5G) communications, novel technologies like reconfigurable intelligent surface (RIS) have emerged to enable intelligent radio environments, thereby further bolstering signal coverage and spectrum management capabilities. Building upon the potential of both CR and RIS, this study endeavors to explore the integration of these concepts within a network to maximize the available benefits. In this system, a secondary source (BS) is responsible for transmitting information to two secondary users, while transmit power constraints are introduced to curtail interference to the primary network caused by cognitive base stations. Monte Carlo simulations are employed to validate the outage probability and throughput expressions. The findings elucidate the impacts of key system parameters and underscore the notable enhancement of the CR network in the presence of a RIS-enhanced primary network.