Transcriptional regulator which functions as a general RNA polymerase II transcription inhibitor. Core component of the 7SK RNP complex: in cooperation with 7SK snRNA sequesters P-TEFb in a large inactive 7SK snRNP complex preventing RNA polymerase II phosphorylation and subsequent transcriptional elongation. May also regulate NF-kappa-B, ESR1, NR3C1 and CIITA-dependent transcriptional activity. Plays a role in the regulation of DNA virus-mediated innate immune response by assembling into the HDP-RNP complex, a complex that serves as a platform for IRF3 phosphorylation and subsequent innate immune response activation through the cGAS-STING pathway. Homooligomer and heterooligomer with HEXIM2; probably dimeric. Core component of the 7SK RNP complex, at least composed of 7SK RNA, LARP7, MEPCE, HEXIM1 (or HEXIM2) and P-TEFb (composed of CDK9 and CCNT1/cyclin-T1). Interacts with the N-CoR complex through NCOR1. Interacts with ESR1 and NR3C1. May interact with NF-kappa-B through RELA. Interacts with CCNT2; mediates formation of a tripartite complex with KPNA2. Part of the HDP-RNP complex composed of at least HEXIM1, PRKDC, XRCC5, XRCC6, paraspeckle proteins (SFPQ, NONO, PSPC1, RBM14, and MATR3) and NEAT1 non-coding RNA. Binds alpha-importin and is mostly nuclear. Widely expressed with higher expression in heart, skeletal muscle and brain (at protein level). Up-regulated by HMBA (hexamethylene bisacetamide). The coiled-coil domain mediates oligomerization. Belongs to the HEXIM family.