Protein kinase component of transcription factor IIH (TFIIH) which phosphorylates the C-terminal domain of RNA polymerase II during transition from transcription to elongation after preinitiation complex (PIC) formation, thereby positively regulating transcription. Essential for both basal and activated transcription, and is involved in nucleotide excision repair (NER) of damaged DNA (By similarity). [DNA-directed RNA polymerase] + ATP = ADP + H(+) + phospho-[DNA-directed RNA polymerase] Component of the TFIIH holo complex. Belongs to the protein kinase superfamily. CMGC Ser/Thr protein kinase family. CDC2/CDKX subfamily.