Cyclin-dependent kinase 12 (CDK12) promotes transcriptional elongation by phosphorylation of the RNA polymerase II C-terminal domain (CTD). Structure-function studies show that this activity is dependent on a C-terminal kinase extension, as well as the binding of cyclin K (CycK). To better define these interactions we determined the crystal structure of the human CDK12/CycK complex with and without the kinase extension in the presence of AMP-PNP. The structures revealed novel features for a CDK, including a large β4-β5 loop insertion that contributes to the N-lobe interaction with the cyclin. We also observed two different conformations of the C-terminal kinase extension that effectively open and close the ATP pocket. Most notably, bound AMP-PNP was only observed when trapped in the closed state. Truncation of this C-terminal structure also diminished AMP-PNP binding, as well as the catalytic activity of the CDK12/CycK complex. Further kinetic measurements showed that the full length CDK12/CycK complex was significantly more active than the two crystallised constructs suggesting a critical role for additional domains. Overall, these results demonstrate the intrinsic flexibility of the C-terminal extension in CDK12 and highlight its importance for both ATP binding and kinase activity.