Apple care

If you are within 30 days of the expiry of your Apple Care+ and are in the U.S, U.K, Australia, Canada, Germany or Japan, you can purchase a recurring monthly extension.

See here: link-> Extend your AppleCare+ coverage - Apple Support

Subject to some inevitable caveats, in many cases you can extend an existing AppleCare+ plan before it expires - but not after. From new, if not purchased immediately, you have 60-days to purchase cover. If cover is interrupted, the plan ends.

Quick and simple answer? No.