Although the Deputy does not say so, I am assuming that he is referring to drivers from Northern Ireland being able to drive into this jurisdiction if Brexit occurs without a deal in place. The answer is that they will.
Specifically, driving across the border in a no-deal Brexit scenario will raise three issues. The first is the driving licence. Under the 1949 Geneva Convention on international road traffic, people will be able to drive here on their Northern Ireland licences, on a visitor basis. No additional documentation will be required in this regard.
Next, there is the question of insurance. There is a international system, pre-dating the EU, under which a so-called 'Green Card' acts as proof of motor insurance in international travel. This system was created to facilitate international road traffic by providing for a single standard document as proof of motor insurance across all participating countries, rather than requiring people to carry different documentation for each country they enter.
Under EU law, Green Cards are not required for travel within the EU. If the UK becomes a Third Country without a deal, the default position will be that Green Cards will be required for UK-registered vehicles entering the EU from the UK. EU law does, however, provide that the EU Commission should set a date after which Green Cards will not be required from a given Third Country, if the Motor Insurers' Bureaux of all the Member States so request. This request was made late last year. The Commission has yet to make a decision on setting a date. Ireland has continued to request that the Commission make a decision, so that Green Cards will not be required.
The third and final matter is whether vehicles should have a national identification sticker. These stickers are prescribed under international road traffic conventions, including the Geneva Convention which I mentioned, and which applies between Ireland and the UK. The purpose of the sticker is largely to identify a vehicle as visiting rather than as based in the jurisdiction, for tax purposes. However, there is no offence of not having a sticker of this kind in Irish road traffic legislation. While I need hardly point out that a person is unlikely to be made liable for vehicle tax simply as a result of not having an international sticker, this is essentially a matter for Revenue. I understand that there is likewise no offence of not having a sticker in UK law.