Ireland does not have a licence exchange agreement with Ukraine. Ukrainian nationals arriving in Ireland under the Temporary Protection Directive (2001/55 EC) will be granted temporary residence. Access to the driving licence system is available with this residency entitlement and Ukrainian refugees can apply for an Irish driving licence in the normal way (sitting the theory test, applying for a learner permit, and passing a driving test).
A person who has held a full Ukrainian driving licence for more than two years can avail of a shorter process to a full licence, involving Essential Driver Training of 6 lessons only, instead of the 12 normally required, and will not have to wait the minimum of 6 months before taking a driving test.
This is a Europe-wide issue which may require a European solution. Ireland has already raised it at EU level with the Transport Directorate, DG Move, and other member states.