Figures from the courts service show 8,008 out of 12,429 motorists convicted of speeding, between May 2017 and May 2019, didn't present their licence in court to have the points recorded.
Just 34 per cent of drivers did, according to figures provided to TD Tommy Broughan.
However Conor Faughnan from the AA says motorists still could face insurance issues if they don't reveal their penalty points.
"Technically speaking the penalty points still apply even if there has been a failure of administration to record them.
"So if for example that person tells their insurance company they don't have any penalty points, that a lie and could affect you if you ever have to make a claim."