Dempsey first came to prominence as a hurler with Ardscoil Rís in Limerick. Having played in every grade as a hurler, he was an unused substitute on 27 February 2011 when Ardscoil Rís retained the Harty Cup title after a 3-19 to 0-03 defeat of C.B.S. Charleville in the final.
Dempsey joined the Na Piarsaigh club at a young age and played in all grades at juvenile and underage levels, enjoying championship success in the under-16, minor and under-21 grades. He made his senior championship debut for the club as a seventeen-year-old in 2013. On 6 October 2013, Dempsey was at right wing-forward when Na Piarsaigh defeated Adare by 0-14 to 0-12 to win the Limerick Senior Championship. He retained his place in the half-forward line for the subsequent Munster Championship, which culminated with him winning a provincial medal after a 4-14 to 0-08 defeat of Sixmilebridge in the final. Dempsey won a second Limerick Championship medal on 11 October 2015 after a 1-22 to 4-12 defeat of Patrickswell in the final. Later that season he won a second Munster Championship medal after a 2-18 to 2-11 defeat of Ballygunner. On 17 March2016, Dempsey won an All-Ireland medal when Na Piarsaigh defeated Ruairí Óg by 2-25 to 2-14 in the final. On 15 October2017, Dempsey won a third Limerick Championship medal when Na Piarsaigh defeated Kilmallock by 1-22 to 2-14 in the final. He later won a third Munster Championship medal when Na Piarsaigh defeated Ballygunner by 3-15 to 2-10 in the final. On 17 March 2018, Casey was named at left wing-forward but played at midfield when Na Piarsaigh were defeated by Cuala in the All-Ireland final. On 27 October 2018, Dempsey won a fourth Limerick Championship medal following Na Piarsaigh's 2-22 to 3-10 defeat of Doon.
Inter-county
Minor and under-21
Dempsey first played for Limerick at minor level. On 23 July 2013, he scored two points when Limerick won their first Munster Championship title in 29 years after a 1-20 to 4-08 defeat of Waterford in the final. Dempsey subsequently joined the Limerick under-21 hurling team in 2015 and won a Munster Championship medal after a 0-22 to 0-19 defeat of Clare in the final. On 12 September 2015, Dempsey was at left wing-forward when Limerick defeated Wexford in the All-Ireland final.
Intermediate
In 2016, Dempsey joined the Limerick intermediate hurling team. On 6 July 2016, he was at right corner-forward when Limerick were defeated by Clare in the Munster final.
Senior
Dempsey joined the Limerick senior hurling team in January 2016. He was an unused substitute throughout the entire season. Dempsey made his senior debut for Limerick on 12 February 2017 in a 1-14 to 0-14 National Hurling League defeat by Wexford. Later that season he made his first championship start, scoring 1-01 in a Munster Championship defeat by Clare. On 19 August2018, Dempsey was a member of the extended panel when Limerick won their first All-Ireland title in 45 years after a 3-16 to 2-18 defeat of Galway in the final. On 31 March 2019, Dempsey was named on the bench for Limerick's National League final meeting with Waterford at Croke Park. He collected a winners' medal as a non-playing substitute in the 1-24 to 0-19 victory.
Career statistics
Honours
;Ardscoil Rís
Harty Cup : 2011
;Na Piarsaigh
All-Ireland Senior Club Hurling Championship : 2016
Munster Senior Club Hurling Championship : 2013, 2015, 2017