How to extend Apple Care?

Are you referring to the standard one year AppleCare warranty which came on your MacBook Pro or are you referring to extending an AppleCare+ plan you purchased within 60 days of original purchase of the device?

Bottom line is if you did not add an AppleCare+ plan to your device within 60 days of original purchase, you cannot extend the standard AppleCare one year plan.

If you did purchase AppleCare+ it can, in some locations be extended. See this link for details about that --> Extend your AppleCare+ coverage - Apple Support

You should be able to extend beyond the 3 year term now on a monthly basis, dependent on parts availability. Within 30 days of the end of your AppleCare+ agreement, you might find the option to extend from your support page if the option is available for your product.

See below for more detail:

Extend your AppleCare+ coverage - Apple Support