Dempsey made his first-team debut for
Carlisle United on 28 January 2014 in a 3–0 win over
Milton Keynes Dons. He was named as Carlisle's Player of the Year for the
2014–15 season. He signed for
Championship club
Huddersfield Town on 10 July 2015 for an undisclosed fee on a three-year contract. He made his debut as an 83rd-minute substitute in a 2–0 defeat against
Hull City at the
KC Stadium on 8 August 2015. He signed for the club permanently on a three-year contract on 19 May 2017. Dempsey joined Fleetwood's League One rivals
Peterborough United on 7 January 2019 on loan until the end of the
2018–19 season. On 17 August 2020, Dempsey joined League One club
Gillingham and was made captain for the 2020-21 season. He was named team captain the following month. Dempsey attracted interest and an offer in the January 2021
transfer window, but Gillingham turned the offer down and Dempsey remained at the club. Dempsey joined
Bolton Wanderers on 31 January 2022 for a fee around £150,000. On 2 April 2023, he started in the
2023 EFL Trophy Final, scoring the opening goal against
Plymouth Argyle; Bolton won 4–0. On 27 June 2023, he signed a two-year extension at Bolton, keeping him at the club until 2026. == Style of play ==