Irish driving licensing legislation is based on a framework of European Union law.
A European Union driving licence is exchangeable for an Irish driving licence, except where the licence issued by the other Member State was itself issued in exchange for a licence from a state that is not a Member State, or a state that Ireland does not have a licence exchange agreement with.
As Ireland does not have a licence exchange agreement with Zimbabwe, a UK licence that was granted in exchange for a Zimbabwean licence cannot be exchanged for an Irish licence.
The Road Traffic (Recognition of Foreign Driving Licences) Order 2007 (S.I. No. 527 of 2007) refers.