The Republic of Ireland has an elected prime minister.
Republic of Ireland . The head of government is the Taoiseach ( Prime Minister , literally ` Chief ' , a title not used in English ) , who is elected by the Dáil and appointed by the President ; the Taoiseach in turn appoints other government ministers . Taoiseach . Taoisigh [ ˈtiːʃi ] , - shee ; [ ˈt̪ˠiː.ʃəx ] ) is the head of government or prime minister of Ireland . The Taoiseach is appointed by the President upon the nomination of Dáil Éireann , the lower house of the Oireachtas ( parliament ) , and must , in order to remain in office , retain the support of a majority in the Dáil .