Fisher entered the Order of Preachers in 1985 and studied for the priesthood in Melbourne, receiving an honours degree in theology from the Yarra Theological Union, a member institution of the Melbourne College of Divinity (now called the University of Divinity).
He worked for a time at Uniya, a centre for social research in Kings Cross, on immigration and refugee issues, and at Holy Name Parish in Wahroonga, Sydney.
He was ordained to the priesthood at Holy Name Church in Wahroonga by Eusebius Crawford OP, Bishop of Gizo, on 14 September 1991.
He undertook doctoral studies in bioethics at the University of Oxford until 1995, matriculating from University College, while residing at Blackfriars Hall.
His Doctor of Philosophy degree was granted for a thesis on "Justice in the Allocation of Healthcare".
His academic work has included lecturing in Australia and overseas and publishing many books and articles on bioethics and morality.
In 1994 he appeared on two British television programs, the bioethics series Brave New World and a special edition of the live discussion program After Dark.

From 1995–2000, Fisher was a lecturer at the Australian Catholic University in Melbourne.
From 2000 to 2003 he was the foundation director of the John Paul II Institute for Marriage and Family in Melbourne, the Australian campus of a postgraduate pontifical institute with nine campuses around the world.
The principal work of the institute was in teaching and research on questions concerning respect for human life and the dignity of the person and support for marriage and family life.
The Australian campus ceased operations in December 2018.

In 2003, Fisher debated euthanasia activist Philip Nitschke at the Great Hall of the University of Sydney.
He is ex officio  chancellor of the Catholic Institute of Sydney (having previously served as the deputy-chancellor) and Adjunct Professor of Bioethics at the University of Notre Dame Australia.
Prior to his episcopal appointment, Fisher was the Master of Students (seminarians) and Socius (deputy) to the prior provincial of the Dominican order in Australia and New Zealand.
In the Melbourne archdiocese, he was Episcopal Vicar for Healthcare, spokesman for the archdiocese on matters of ethics, a visiting lecturer at the Catholic Theological College and secretary to the Senate of Priests.
His community engagements have included being Chaplain to the Parliament of Victoria, a member of the Infertility Treatment Authority of Victoria, chair or member of several hospital ethics committees, a conventual chaplain ad honorem to the Sovereign Military Order of Malta and a chaplain to various other organisations.
He has also had various engagements in parish life and the pastoral care of the handicapped and the dying.
Fisher entered the Order of Preachers in 1985 and studied for the priesthood in Melbourne, receiving an honours degree in theology from the Yarra Theological Union, a member institution of the Melbourne College of Divinity (now called the University of Divinity). He worked for a time at Uniya, a centre for social research in Kings Cross, on immigration and refugee issues, and at Holy Name Parish in Wahroonga, Sydney. He was ordained to the priesthood at Holy Name Church in Wahroonga by Eusebius Crawford OP, Bishop of Gizo, on 14 September 1991. He undertook doctoral studies in bioethics at the University of Oxford until 1995, matriculating from University College, while residing at Blackfriars Hall. His Doctor of Philosophy degree was granted for a thesis on "Justice in the Allocation of Healthcare". His academic work has included lecturing in Australia and overseas and publishing many books and articles on bioethics and morality. In 1994 he appeared on two British television programs, the bioethics series Brave New World and a special edition of the live discussion program After Dark.
From 1995–2000, Fisher was a lecturer at the Australian Catholic University in Melbourne. From 2000 to 2003 he was the foundation director of the John Paul II Institute for Marriage and Family in Melbourne, the Australian campus of a postgraduate pontifical institute with nine campuses around the world. The principal work of the institute was in teaching and research on questions concerning respect for human life and the dignity of the person and support for marriage and family life. The Australian campus ceased operations in December 2018.
In 2003, Fisher debated euthanasia activist Philip Nitschke at the Great Hall of the University of Sydney. He is ex officio  chancellor of the Catholic Institute of Sydney (having previously served as the deputy-chancellor) and Adjunct Professor of Bioethics at the University of Notre Dame Australia. Prior to his episcopal appointment, Fisher was the Master of Students (seminarians) and Socius (deputy) to the prior provincial of the Dominican order in Australia and New Zealand. In the Melbourne archdiocese, he was Episcopal Vicar for Healthcare, spokesman for the archdiocese on matters of ethics, a visiting lecturer at the Catholic Theological College and secretary to the Senate of Priests. His community engagements have included being Chaplain to the Parliament of Victoria, a member of the Infertility Treatment Authority of Victoria, chair or member of several hospital ethics committees, a conventual chaplain ad honorem to the Sovereign Military Order of Malta and a chaplain to various other organisations. He has also had various engagements in parish life and the pastoral care of the handicapped and the dying.
Anthony Fisher