As a novel technology, simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) provides users with full spatial coverage communication by modulating reflected and refracted signals. This study proposes a novel UAV equipped with STAR-RIS-assisted non-orthogonal multiple access system that jointly optimized the cluster correlations with the power allocation coefficients and positions of STAR-RIS to maximize the user system sum rate. However, the application of this technique is limited by the complex nonconvex optimization problem, which was addressed by developing an alternating optimization iteration algorithm. The joint optimization problem related to cluster association and the power allocation coefficients and positions of STAR-RIS was solved by alternating iterations. The simulation results demonstrated that the proposed algorithm delivered a superior user system sum rate compared to single-power optimization, ultimately achieving near-optimal system performance. At the same time, we verified that the NOMA system equipped with STAR-RIS on UAV can achieve the best performance than the OMA system. Therefore, the proposed algorithm contributes to the optimization of STAR-RIS-assisted systems, which will benefit applications in wireless communications, IoT, and smart city infrastructure.