Cluskey is educated at St. Vincent’s C.B.S. in Glasnevin. He works as a butcher and then joins the Labour Party. He quickly becomes a branch secretary in the Workers’ Union of Ireland. At the 1965 general election he is elected as a Labour Party Teachta Dála (TD) for the Dublin South-Central constituency. In 1968 he is elected Lord Mayor of Dublin. In 1973 he is appointed Parliamentary Secretary to the Minister for Social Welfare, Brendan Corish. He introduces sweeping reforms to the area while he holds that position. He plays a leading role in initiating the EU Poverty Programmes.
The Fine Gael–Labour Party coalition is defeated at the 1977 general election resulting in the resignation of Brendan Corish as Labour Party leader. Cluskey is elected the new leader of the Labour Party. In 1981, the Labour Party enters into a coalition government with Fine Gael. However Cluskey has lost his seat in Dáil Éireann at the 1981 general election and with it the party leadership. He is appointed on July 1, 1981 as a Member of the European Parliament (MEP) for Dublin, replacing Michael O’Leary, who had resigned the seat after succeeding Cluskey as Labour leader.
The coalition government falls in January 1982 over a budget dispute, and Cluskey is re-elected to the Dáil at the February 1982 general election. When the coalition returns to office after the November 1982 election, Cluskey is appointed as Minister for Trade, Commerce and Tourism. He then resigns from the European Parliament, to be replaced by Brendan Halligan.
On December 8, 1983 Cluskey resigns as Minister due to a fundamental disagreement over government policy about the Dublin Gas Company. He retains his Dáil seat in the 1987 general election.
Following his re-election Cluskey’s health begins to deteriorate. He dies in Dublin on May 7, 1989 following a long battle with cancer.