This letter investigates covert communication in uplink NOMA systems assisted by an energy harvesting jammer (EHJ), where a reliability-required user (RRU) and a covertness-required user (CRU) are paired to perform NOMA to transmit messages to Bob, in the presence of a warden (Willie) who tries to detect CRU’s transmission behavior. In particular, the EHJ with time switching (TS) scheme has been employed for the purpose of confusing Willie and compensating for the energy supply. We derive the closed-form expressions of expected minimum detection error probability (EMDEP) and connection outage probabilities (COPs) at RRU and CRU, then we analyse the maximum effective covert rate (ECR) under the covertness and RRU’s quality of service (QoS) constraints. Our analysis indicates that there exist an optimal transmit power at Bob and time switching factor to maximize the maximum ECR, and RRU’s QoS constraint has a remarkable effect on the maximum ECR as the transmit power at Bob or time switching factor increases.