Around 3,000 holders of UK driving licences resident in Ireland have yet to swap their UK licence for an Irish one, according to insurance industry estimates, meaning they are no longer licensed to drive in Ireland.
The Department of Transport has said that to date about 67,000 people have exchanged their UK permit for an Irish licence.
The mechanism that allowed for the recognition and exchange of UK licences for an Irish one expired at the end of the Brexit transition period last night but has now been extended.
Residents with UK driving licences may still swap for Irish licences after Minister for Transport Eamon Ryan signed an agreement with the UK that will allow for the exchange.
The Department of Transport said: "This agreement will be of particular benefit to anyone planning to live in Ireland as it will allow them to exchange their UK licence for an Irish driving licence.
"It will also allow anyone who has not exchanged their UK licence in time, before the deadline of 11pm on the 31 December, to exchange it under this new agreement."
But for anyone who did not exchange their UK licence by the deadline, their UK licence will no longer be valid to drive here in Ireland, it is only valid for exchange purposes.
The Department of Transport said it is imperative that it be exchanged immediately.
This change does not affect people with UK licences living in Northern Ireland or Great Britain who are visiting or driving in Ireland.
Meanwhile the EU and UK have agreed to respectively recognise each other's driver licences for citizens visiting members states or the UK.