Ireland does not have a driving licence exchange agreement with Ukraine. Ukrainian citizens entering Ireland under the Temporary Protection Directive (2001/55 EC) can apply for an Irish licence in the normal way, by obtaining a learner permit and then sitting a practical test.
People who have held a full Ukrainian licence for more than two years can avail of the shorter Essential Driver Training of 6 lessons, instead of the usual 12, and 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.