Aurora-A regulates the recruitment of TACC3 to the mitotic spindle through a phospho-dependent interaction with clathrin heavy chain (CHC). Here, we describe the structural basis of these interactions, mediated by three motifs in a disordered region of TACC3. A hydrophobic docking motif binds to a previously uncharacterized pocket on Aurora-A that is blocked in most kinases. Abrogation of the docking motif causes a delay in late mitosis, consistent with the cellular distribution of Aurora-A complexes. Phosphorylation of Ser558 engages a conformational switch in a second motif from a disordered state, needed to bind the kinase active site, into a helical conformation. The helix extends into a third, adjacent motif that is recognized by a helical-repeat region of CHC, not a recognized phospho-reader domain. This potentially widespread mechanism of phospho-recognition provides greater flexibility to tune the molecular details of the interaction than canonical recognition motifs that are dominated by phosphate binding.