The Dual connectivity (DC) technology is a robust solution for Internet service providers (ISP) to evolve their legacy infrastructures with less cost to speed up the progress of fifth-generation (5G) services coverage. DC enables the traditional network to connect to multiple New Radio (NR) Node B (gNBs). A well-known scheme is the non-standalone (NSA) NR. In this case, the user equipment (UEs) could access the network via both the evolved Node B (eNB) and the gNB. However, some research has indicated that the UEs in such a configuration suffer from power consumption problems. UEs are typically configured with discontinuous reception (DRX) mechanism to save power. However, most current systems do not investigate and optimize the DRX parameters. To the authors’ best knowledge, this work is the first to combine DRX with traffic steering for the UEs in the NSA NR system. A traffic steering algorithm is proposed to improve the coordination between the eNB and the gNB. We used a semi-Markov chain model to analyze power consumption and average delay. Compared with standard DRX operated in LTE, NR, and DC, we verified that the proposed model achieves power-saving gains without incurring an additional delay. The results indicated that the UE could save considerable power with an optimized system configuration.