Irish driving licensing law operates within a framework of EU law. Under the EU Directive on driving licences and the relevant Irish regulations, driving licences issued by Member States are mutually recognised. The Directive stipulates that a person may not hold more than one driving licence, thus requiring that, in this case, the person must surrender their UK licence when exchanging it for an Irish one.
While the UK is still a Member State, a person may exchange their UK licence for an Irish licence, as both are EU licences. When a Member State licence is presented here for exchange, the licensing authority of that Member State is notified that the licence has been exchanged for an Irish licence.
In the event of a no-deal Brexit the driving licence of a UK licence holder living here in Ireland will not be recognised and the driver will not be able to continue to drive here in Ireland on that licence.
Legislation in the Road Traffic Acts allows for the recognition of foreign driving licences for exchange purposes. If there is a no deal Brexit, the UK becomes a 3rd country and the potential then exists for arrangements to be made under this legislation. Ireland will be actively pursuing this option however, this may take a little time to complete as it involves a formal agreement and legislation here in Ireland. However, the same principle applies regarding one licence being exchanged for another.