Bishop Walsh was ordained a priest of the Diocese of Scranton by Bishop James C. Timlin at the Cathedral of Saint Peter, Scranton, Pa., on June 25, 1994. After ordination, Bishop Walsh served as assistant pastor at Saint Rose of Lima Church, Carbondale, and the Cathedral of Saint Peter, Scranton. In July 1999, he was appointed to his first pastorate at Saint Mary of the Lake Church, Lake Winola, as well as Director of Spiritual & Liturgical Formation at Saint Pius X Seminary in Dalton, Pa.. From July 2004-July 2006, he served as pastor at Nativity of the Blessed Virgin Mary Church, Tunkhannock, until being appointed to serve as Episcopal Vicar for the Eastern Pastoral Region of the Diocese of Scranton.
In 2008, Bishop Walsh became administrator of Saint Rita Church, Gouldsboro, and in 2009 was appointed administrator of Saint Anthony, Saint Bridget and Saint John the Baptist parishes in Throop. In July 2010, Bishop Walsh was appointed to serve as pastor at the Church of Saint John, East Stroudsburg.
In January 2015, he was appointed Episcopal Vicar for Clergy by Bishop Joseph C. Bambera. While serving in that role, Bishop Walsh also served as Sacramental Minister for Our Lady of the Eucharist Parish, Pittston. In July 2020, he was appointed pastor at Saint Rose of Lima Parish, Carbondale, and Our Lady of Mount Carmel Parish, Carbondale.
On December 21, 2021, the Diocese of Gaylord, Mich., announced that Bishop Walsh had been appointed by Pope Francis to serve as sixth bishop of the Diocese of Gaylord.