You should have a change of ownership form (RF101) which is usually attached to the Registration Certificate ("Logbook"). The Dept. of Transport would have sent you this when you bought it. When you sell the car, you need to get the new buyers name, address, contact details etc, and fill out the form and send it back to them in Shannon. Once they receive the form, they enter it on the system and the change of ownership is noted.
However, bear in mind that Penalty points are issued to the 'driver' and not the 'owner' of the car (there may be some offences for which the owner is liable, not sure?). If someone is stopped for speeding in your car, they get Points on their licence.