Thomas Clarke Moore was born in Cincinnati, Ohio on September 16, 1930 to Clark and Mary Ellen Bidwill Moore. He was the oldest of three sons and a daughter, Richard and William survived him, but his sister Veronica died before him. Thomas entered Quigley Preparatory Seminary in Chica go, Illinois, to become of priest of the Archdiocese of Chicago but his health did not allow him to continue in the seminary. He continued his college studies at De Paul University in Chicago and one year later entered the Order.

He made his novitiate at St. Peter Martyr Priory in Winona, Minnesota, in 1950 and was given the name Alexander. He made his profession of vows on August 31, 1951 and was transferred to the Dominican House of Studies in River Forest for his philosophy studies. He was a good student and obtained advanced degrees in philosophy. After completing his studies in theology at St. Rose of Lima Priory, he was ordained a priest on May 25, 1957.

His superiors noting his intellectual ability sent him to the Universit de Fribourg in Switzerland where he obtained a Doctorate in Sacred Theology. Immediately he was sent to study at the Oriental Institute at the Catholic University of America to master biblical languages, he received the S.S.B and S.S.L. degrees from the Pontifical Biblical Commission in Rome in 1964. From 1964 to 1966, he did advanced scripture studies at the cole Biblique in Jerusalem, Israel.

From 1966 to 1975, he was a member of the faculty of Aquinas Institute of Theology in Dubuque, Iowa as a teacher of Sacred Scripture. Over time he lost interest in the intellectual apostolate and sort a new direction. He became the pastor of Saint Pius V Parish in Chicago, which had now become a Spanish speaking parish with a large immigrant population, he was noted for his efforts in social justice issues during his tenure.

In 1980, he moved to Tucson, Arizona, to work in the campus ministry of the University of Arizona and be near his aged parents who needed his attention. Three years later he became a Parochial Vicar in Saint Pius X Parish in Tucson. After the death of his parents and sister, he returned to a ministry of the province at the campus ministry of the University of New Mexico. In 1991, he moved on to working in parishes of the Archdiocese of Santa Fe and became more distant from the province community.

In 2002, he returned to Tucson, Arizona in retirement with residence at Saint Pius X Parish. He would celebrate the sacraments and offer adult education classes on a limited basis due to health problems. On July 5, 2009, when he did not appear to celebrate the Eucharist at the parish, he was discovered dead in his residence. The wake service and Mass of Christian Burial was held at Saint Pius X Parish by the people of the parish and he was buried in the Dominican Plot at All Saints Cemetery in Des Plaines, Illinois.