Telomere maintenance requires extension of the G-rich telomeric repeat strand by telomerase and fill-in synthesis of the C-rich strand by Polα/Primase. Telomeric Polα/Primase is bound to Ctc1-Stn1-Ten1 (CST), a single-stranded DNA-binding complex. Like mutations in telomerase, mutations affecting CST-Polα/Primase result in pathological telomere shortening and cause a telomere biology disorder, Coats plus (CP). We determined cryogenic electron microscopy structures of human CST bound to the shelterin heterodimer POT1/TPP1 that reveal how CST is recruited to telomeres by POT1. Phosphorylation of POT1 is required for CST recruitment, and the complex is formed through conserved interactions involving several residues mutated in CP. Our structural and biochemical data suggest that phosphorylated POT1 holds CST-Polα/Primase in an inactive auto-inhibited state until telomerase has extended the telomere ends. We propose that dephosphorylation of POT1 releases CST-Polα/Primase into an active state that completes telomere replication through fill-in synthesis.