How to unlock old iPhones before selling them

If the phone is indeed carrier locked, you would need to follow the steps at: How to unlock your iPhone for use with a different carrier - Apple Support

Removing the SIM card removes the information that the phone needs to access a particular cellular plan. It will not, however, remove a carrier lock. If the phone is locked into receiving service from a particular phone company (e.g., AT&T), only that carrier can release the lock.