As the demand for high-performance wireless communication continues to grow, it becomes essential to explore efficient network designs that can improve system efficiency, coverage, and capacity. In this letter, we investigate the performance of hybrid active relays and reconfigurable intelligent surfaces (HARRIS)-aided non-orthogonal multiple access (NOMA) networks. We derive the outage probability of the proposed HARRIS architecture in closed-form expression over Rician fading channels and develop a framework for selecting the best HARRIS node considering different quality of service (QoS) requirements of the users. Simulation results include comparisons with pure RIS and pure relay in both NOMA and orthogonal multiple access (OMA) networks. Under favorable path loss, HARRIS approaches pure RIS performance, while in severe path loss, it closely aligns with purely active relay. Moreover, OMA outperforms NOMA for low QoS requirements, but NOMA excels in high QoS scenarios.