Can I buy AppleCare for my 2021 MacBook Pro after 60 days

What is NOT covered by warranty alone is screen glass breakage, liquid spills, or catastrophic failure (hard drops or "run over by a truck"). If you wanted the extended coverage, you must have signed up within 60 days, and an inspection or remote diagnostic may be required.

Some users will have No claims during this period. This "insurance effect" allows the manufacturer to keep the price of this service contract relatively low. You generally can not sign up later, because then only owners with problems would sign up, after they discovered an issue.

No, it has to be Within 60 days of original purchase.

If a second answer will help. No, no you can't.