The Republic
The Republic of Ireland Act amounted to a final declaration of an Irish republic. Irish membership of the Commonwealth of Nations automatically lapsed. The then government, under John A. Costello opted not to reapply for membership, a decision criticised by then Leader of the Opposition Eamon de Valera, who considered applying for membership in the 1950s. (De Valera's grandson, Eamon O'Cuiv, now an Irish government minister, in the 1990s again advocated Irish membership of the Commonwealth.)
In the 1990s the All Party Oireachtas Committee on the Constitution considered amending Bunreacht na hÉireann to mention that Ireland is a republic. It decided against, eventually.