The CST complex (CTC1-STN1-TEN1) has been shown to inhibit telomerase extension of the G-strand of telomeres and facilitate the switch to C-strand synthesis by DNA polymerase alpha-primase (pol α-primase). Recently the structure of human CST was solved by cryo-EM, allowing the design of mutant proteins defective in telomeric ssDNA binding and prompting the reexamination of CST inhibition of telomerase. The previous proposal that human CST inhibits telomerase by sequestration of the DNA primer was tested with a series of DNA-binding mutants of CST and modeled by a competitive binding simulation. The DNA-binding mutants had substantially reduced ability to inhibit telomerase, as predicted from their reduced affinity for telomeric DNA. These results provide strong support for the previous primer sequestration model. We then tested whether addition of CST to an ongoing processive telomerase reaction would terminate DNA extension. Pulse-chase telomerase reactions with addition of either wild-type CST or DNA-binding mutants showed that CST has no detectable ability to terminate ongoing telomerase extension in vitro. The same lack of inhibition was observed with or without pol α-primase bound to CST. These results suggest how the switch from telomerase extension to C-strand synthesis may occur.