Clancy was born in Lithgow, New South Wales, on 13 December 1923. He said that he wanted to be a priest from an early age and pretended to celebrate his first Mass while still a child, to the amusement of his brother and sisters. After completing his studies at Marist Brothers College, Parramatta, he was ordained to the priesthood in 1949, on the same day as the future Australian cardinal Edward Cassidy.
Priest and bishop
In 1953 Clancy earned a Licentiate in Sacred Theology from the Pontifical University of St Thomas Aquinas. Clancy continued his education, eventually earning his doctorate in theology in 1965. He then started as a teacher and later accepting the position of chaplain at the University of Sydney. He also served as the official spokesperson for the archdiocese at this time and became very well known on that basis. On 19 January 1974, Clancy was consecrated titular Bishop of Árd Carna and Auxiliary Bishop of Sydney.
Archbishop and cardinal
On 24 November 1978, he was appointed Archbishop of Canberra. In the little over four years that he was Archbishop of Canberra and Goulburn, Clancy was respected by the people of Canberra Goulburn as a very friendly and approachable archbishop who was also very supportive of his people and his priests. He had a great rapport with young people in the archdiocese. On 12 February 1983 he was appointed Archbishop of Sydney and on 28 June 1988 he was elevated to Cardinal-Priest of Santa Maria in Vallicella. He also continued his education career throughout this time, becoming the Chancellor of the Australian Catholic University in 1992. Major work on St Mary's Cathedral, Sydney took place under his episcopacy. In 1999 a substantial new pipe organ was built by Orgues Létourneau Ltée of Montreal, Québec. In the year 2000 the spires of the cathedral were finally completed. During his term as archbishop the neo-Gothic diocesan seminary of St Patrick's at Manly was closed and the heritage listed building leased to an international hospitality school. A new seminary, the Seminary of the Good Shepherd, was opened in the inner-western Sydney suburb of Homebush. Cardinal Clancy was a Fellow of Warrane College, UNSW.
Abuse scandal
His tenure was not without controversy because of allegations surrounding the abuse scandal within his diocese.
Retirement and death
Clancy retired as Archbishop of Sydney in 2001 and was succeeded by Archbishop George Pell. In the period from 21 October 2003 until Clancy's own 80th birthday on 13 December 2003, there were three Australian cardinal electors ; Clancy, Pell and Edward Cassidy. Clancy's health began to decline after his retirement and he died on 3 August 2014, aged 90, at the Little Sisters of the Poor nursing home in the Sydney suburb of Randwick.