Burke plays his club hurling with St Thomas'. His honours include a County Minor A Championship from 2008 and also a County U-21 A Championship from 2011. Burke was captain of the St. Thomas's team on both occasions. David Burke also won a County Senior championship in 2012 and an All Ireland Club championship in 2013. He won another county total in 2016 but unfortunately lost to Ballyaodh in the All Ireland club semi-finals. In 2018 he won another county total beating Liam Mellows. He went on to the All-Ireland club final only to lose to Ballyhale Shamrocks of Kilkenny. He once again went on to beat Liam Mellows in the 2019 County Hurling final.
Inter-county
Burke first came to prominence on the inter-county scene as a member of the Galway minor hurling team. In 2008 he lined out in the All-Ireland final, however, Kilkenny accounted for the westerners. Two years later Burke had joined the Galway under-21 team and lined out in that year's championship decider. Burke made his senior debut in championship against Wexford which many believed would be a success for him and his team after they were crowned National Hurling League champions. He is probably described by many as the best midfielder in the game. In 2011, Burke was a key member of the victorious Galway All-Ireland Under 21 Championship winning team. In 2012, Burke was an ever present member of the Galway team which won the Leinster Senior Hurling Championship for an historic first time. He played at right half forward on the Galway team which defeated Kilkenny on a scoreline of 2-21 to 2-11. Burke scored one of the most memorable points of the Championship in the second half of the Leinster final against Kilkenny, which ended in that historic victory for the county. His performances continued to be outstanding in Galway's run to the All-Ireland Final, where they were defeated by Kilkenny after a replay. In October 2012, as recognition for his terrific season for the county, Burke received his first All Star Award. In 2015, Burke was a key player at midfield in Galway's run to the All-Ireland Final, where they were defeated by Kilkenny. His form in the championship earned him his second All-Star Award in November 2015. At the beginning of the 2016 season, Burke became captain of the Galway senior hurling team. In November 2016, Burke received his third All-Star award after another outstanding year. On 22 April 2017, Burke captained Galway to win the 2017 National Hurling League after a 3-21 to 0-14 win against Tipperary in the final. On 3 September 2017, he captained Galway to their first All-Ireland Senior Hurling Championship win for 29 years.
