The special telomere repairing protein (telomerase) is active in Humans. It's what resets the telomere length in embryos, and it's also active (but not enough to fully replenish them) in any body tissues that need to regenerate.

One place it's fully active is in cancer cells. It's theorized one of the functions of shortening telomeres is to prevent cancer, because any cancer starting to grow will burn through its telomeres and die, unless the cancer cell is able to mutate to repair its telomeres.