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In this paper, we carry out the performance analysis of the simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) in the hybrid automatic repeat request (HARQ) assisted cognitive non-orthogonal multiple access (NOMA) networks, where a security-required user (SRU) with secure transmission requirements is paired with a quality of service (QoS)-sensitive user (QSU) with low delay requirements to perform NOMA. To characterize the performance of secure transmission, we derive the analytical expressions for connection outage probability (COP), average number of transmission (ANT) and secrecy outage probability (SOP) for the SRU in randomized retransmission NOMA (RR-NOMA) scheme, while a cognitive power allocation scheme is developed to meet QSU’s QoS requirement. To obtain deeper insights, the asymptotic expressions of COP and SOP are also derived …