there is no need for any license for any gun in NH
For handguns, a P&R license is required for a sale face to face UNLESS the buyer is personally known to you.
I do not think that is required for long arms, but you want to be reasonably sure that the person you are selling to is not a prohibited person, so you need to know the person, have someone you know and trust assure you the buyer is legal, or if in doubt, transfer the gun via a FFL who will do a background check