Following ordination, Dempsey's first pastoral appointment was as a
curate in
Clane and
Rathcoffey. Seven years later, he was appointed curate in
Kildare, and simultaneously as diocesan youth director and director of vocations. During his time as diocesan youth director, Dempsey organised two
World Youth Day pilgrimages in
2005 and
2008. It was during his curacy in Kildare that he also started writing a weekly article in the
Leinster Leader and presenting
Religion Matters, a religious and social affairs program on
Kfm. Dempsey returned to the Milltown Institute for further studies, completing a
master's degree in theology in 2008. His thesis examined whether the Catholic Church in contemporary Ireland was a church in crisis or one in question. Dempsey was appointed to the parish cluster of
Naas,
Sallins and Two Mile House in 2009, before moving to
Newbridge in August 2014, when he was also appointed
vicar forane for the North deanery. The following year, Dempsey was appointed parish priest in Newbridge and simultaneously
administrator in
Caragh and
Prosperous. In a December 2010 article for
The Furrow on being a priest in modern Ireland, Dempsey wrote that "the Church community needs to enter into a period of deep reflection", adding that it would be "refreshing to see some leadership around this 'reflection' culminating in some form of national Church gathering", and noting his awareness of major issues in the church, such as the role of women and the appointment of bishops. == Episcopal ministry ==