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.

The following year, Dempsey was appointed parish priest in Newbridge and simultaneously administrator in Caragh and Prosperous.

[11] His episcopal ordination was initially scheduled to take place on 19 April, but was rescheduled on 17 June due to the COVID-19 pandemic.

[12][13][14] Dempsey was eventually consecrated by the Archbishop of Tuam, Michael Neary, on 30 August in the Cathedral of the Annunciation of the Blessed Virgin Mary and St Nathy, Ballaghaderreen.

The Bishop of Elphin, Kevin Doran, was subsequently appointed as apostolic administrator sede vacante of the Diocese of Achonry.