In 2014, Dempsey made his first team debut for Carlisle United, where he was named as Carlisle's Player of the Year for the 2014–15 season. Over the next few years, he would go on to play for Huddersfield Town and Fleetwood Town, before moving to Gillingham, where he was named captain.

On 31 January 2022, Dempsey joined Bolton Wanderers.

In particular during the second half of the 2022-23 season, Dempsey impressed with consistent performances and was rewarded with a twp-year contract extension to take his deal to 2026.