You can apply in person at any of the 36 National Driver Licence Service (NDLS) centres nationwide.
If you have a Public Services Card (PSC) you can use it with a verified MyGovID to apply online. If you apply at an NDLS centre, you can use your PSC to simplify the process as it will satisfy the following requirements:
If you do not have a PSC you are required to present documentation at the NDLS Centre to satisfy 1. Photo ID, 2. Evidence of PPSN, 3. Evidence of Address, 4. Evidence of normal residence - see above for a list of acceptable documents for each.
In some cases the same document may satisfy more than one requirement e.g. an Irish/EU passport is adequate as photo ID & proof of residency entitlement; a letter to you from Revenue which shows your PPSN could be used as both proof of your address & proof of your PPSN.