Motorists resident in Ireland with a UK driving licence are being advised to exchange that licence for an Irish driving licence before the 29 March 2019. The Department has always advised people to exchange their EU driving licence for an Irish driving licence once they become a resident of Ireland.
Currently, a UK licence is recognised as an EU licence and that is why it can be accepted by Irish insurance companies. In the event of a no deal Brexit, this will no longer be the case. Irish driver licensing law operates within a framework of EU law.
In the case of non-EU jurisdictions, legislation exists, under the Road Traffic Acts, to allow 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 the Road Traffic Acts. Ireland will be pursuing this option. This may take a little time to complete as it involves a formal agreement and legislation here in Ireland.