Nonorthogonal multiple access (NOMA) and cognitive integrated satellite terrestrial relay networks are the promising and key part for the next-generation wireless networks. This article researches the joint effects of channel estimation errors (CEEs) and hardware impairments on the secrecy performance of cognitive integrated satellite terrestrial relay networks. The noncolluding eavesdropping scheme is applied in the multiple eavesdroppers, where the eavesdropper with the highest eavesdropping capacity is selected to overhear the legitimate transmission signal. Moreover, the detailed analysis for the secrecy outage probability (SOP) is obtained based on the utilized partial terrestrial relay selection strategy. To obtain the insightful conclusions, the asymptotic analysis along with the secrecy coding gain and secrecy diversity order for the SOP are further derived, which gives the effective methods to valuate the impacts of CEEs and hardware impairments on the considered system with the NOMA scheme in high signal-to-noise ratio regime. Moreover, simulations are derived for the secrecy energy efficiency. Finally, Monte Carlo simulations are given to prove the correctness of the theoretical SOP analysis.