I'm thinking of buying a 230/15 amp air conditioner to replace an older one. The current connection is 230/20 amp. What do I need to do to make this work?

Should be able to just plug the new a/c into your outlet with out changing anything.

Perhaps change the plug if it is a different type or style.

A 20 amp breaker will not protect a 15 amp unit.
Change breaker to 15amp.

Chuck