Are some sort of clamps supposed to be left in after a surgery?

Sometimes. Certain procedures do leave things inside of you. Staples are very common. Orthopedic and neurosurgical procedures commonly leave things inside of you. "clamp" is not very specific so it's hard to say what you might be calling a clamp. Staples clamp blood vessel. There are clamps that are left behind to seal the ends of intestines. Time to ask your doc for more info.