"Republic of Ireland."
Translation:Poblacht na hÉireann.
This is the genitive case of Éire, and is used to signify the 'of' in the English translation. Also, it's worth noting that in native speech Éire is not used as the nominative case; native speakers would use Éirinn instead.
Standard: Tá Éire go hálainn
Natives: Tá Éirinn go hálainn