Hyperphosphorylation of the C-terminal domain (CTD) of the RPB1 subunit of human RNA polymerase (Pol) II is essential for transcriptional elongation and mRNA processing1-3. The CTD contains 52 heptapeptide repeats of the consensus sequence YSPTSPS. The highly repetitive nature and abundant possible phosphorylation sites of the CTD exert special constraints on the kinases that catalyse its hyperphosphorylation. Positive transcription elongation factor b (P-TEFb)-which consists of CDK9 and cyclin T1-is known to hyperphosphorylate the CTD and negative elongation factors to stimulate Pol II elongation1,4,5. The sequence determinant on P-TEFb that facilitates this action is currently unknown. Here we identify a histidine-rich domain in cyclin T1 that promotes the hyperphosphorylation of the CTD and stimulation of transcription by CDK9. The histidine-rich domain markedly enhances the binding of P-TEFb to the CTD and functional engagement with target genes in cells. In addition to cyclin T1, at least one other kinase-DYRK1A 6 -also uses a histidine-rich domain to target and hyperphosphorylate the CTD. As a low-complexity domain, the histidine-rich domain also promotes the formation of phase-separated liquid droplets in vitro, and the localization of P-TEFb to nuclear speckles that display dynamic liquid properties and are sensitive to the disruption of weak hydrophobic interactions. The CTD-which in isolation does not phase separate, despite being a low-complexity domain-is trapped within the cyclin T1 droplets, and this process is enhanced upon pre-phosphorylation by CDK7 of transcription initiation factor TFIIH1-3. By using multivalent interactions to create a phase-separated functional compartment, the histidine-rich domain in kinases targets the CTD into this environment to ensure hyperphosphorylation and efficient elongation of Pol II.