Member of the cyclin-dependent kinase pair (CDK9/cyclin-T) complex, also called positive transcription elongation factor B (P-TEFb), which is proposed to facilitate the transition from abortive to production elongation by phosphorylating the CTD (C-terminal domain) of the large subunit of RNA polymerase II (RNAP II) and SUPT5H. ATP + L-seryl-[protein] = ADP + H(+) + O-phospho-L-seryl-[protein] ATP + L-threonyl-[protein] = ADP + H(+) + O-phospho-L-threonyl-[protein] [DNA-directed RNA polymerase] + ATP = ADP + H(+) + phospho-[DNA-directed RNA polymerase] Associates with cyclin-T to form P-TEFb. Belongs to the protein kinase superfamily. CMGC Ser/Thr protein kinase family. CDC2/CDKX subfamily.