In this paper, we investigate the outage behavior of a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-empowered cognitive non-terrestrial vehicle network with non-orthogonal multiple access (NOMA), in which Rician fading channels and imperfect/perfect successive interference cancellation (ipSIC/pSIC) are considered. In the network, STAR-RIS is utilized to assist the transmission and reflection of the superposed signals from a secondary unmanned aerial vehicle. Under the interference constraints of primary vehicle users, we derive the exact expressions of outage probability for all secondary vehicle users to evaluate the system parameters. Moreover, to gain deeper insights, the asymptotic expressions of outage probability along with the diversity order are obtained. Then, from numerical results, we confirm the correctness of our theoretical analysis and discuss the influences of key parameters on system performance. Compared with STAR-RIS-orthogonal multiple access (OMA)/non-STAR-RIS scheme, the superiority of our scheme is verified.