Kelly first came to prominence on the intr-county scene as a member of the Clare minor team in 2010. He won his first Munster medal that year following a 1-16 to 1-11 defeat of Waterford. Clare subsequently qualified for the All-Ireland decider against Kilkenny, however, Kelly's side faced a narrow 2-10 to 0-14 defeat. In 2011 Kelly was appointed captain of the Clare minor team. He won a second consecutive Munster medal that year following a 1-20 to 3-9 defeat of Waterford once again. The subsequent All-Ireland semi final saw Clare defeated by Galway after extra time. Kelly also became a member of the Clare under-21 team in 2011, however they were defeated in the Munster Semi-final by Limerick on a scoreline of 2-19 to 1-15 despite a contribution of 3 points from play from Tony Kelly. This remains Kelly's only defeat in the Munster Minor and Under-21 Championships. Kelly won his first Munster medal in that grade as Clare defeated Tipperary by 1-16 to 1-14 in the 2012 Munster Final in Cusack Park in Ennis. After trailing at half-time, Clare outscored Kilkenny by 1-10 to 0-4 in the second period of play to secure a 2-17 to 2-11 victory in the All-Ireland final of the same year. It was Kelly's first All-Ireland medal in the grade. Clare dominated the under-21 series once again in 2013. A 1-17 to 2-10 defeat of Tipperary in the provincial decider gave Kelly a second Munster medal. The subsequent All-Ireland saw Clare face first-time finalists Antrim. In a complete mismatch, Clare powered to a 2-28 to 0-12 victory, with Kelly collecting a second consecutive All-Ireland medal.
Senior
Kelly made his senior championship debut at left wing-forward and scoring 1-2 in a 1-16 to 0-16 defeat of Dublin on 7 July 2012. On 8 September 2013 Kelly lined out against Cork in his first All-Ireland final. Three second-half goals through Conor Lehane, Anthony Nash and Pa Cronin, and a tenth point of the game from Patrick Horgan gave Cork a one-point lead as injury time came to an end. A last-gasp point from corner-back Domhnall O'Donovan earned Clare a 0-25 to 3-16 draw. The replay on 28 September was regarded as one of the best in recent years. Clare's Shane O'Donnell was a late addition to the team, and went on to score a hat-trick of goals in the first nineteen minutes of the game. Horgan top scored for Cork, however, further goals from Conor McGrath and Darach Honan secured a 5-16 to 3-16 victory for Clare. It was Kelly's first All-Ireland medal. He rounded off the season by collecting his first All-Star award, while also becoming the only player in the history of the scheme to have won the Hurler and Young Hurler of the Year awards in the same year. In June 2014, Kelly featured in the Sky Sports television advert to promote their new broadcasting deal with the GAA. On 8 May 2016, Clare won the 2016 National Hurling League, their first National Hurling League title since 1978 after a 1-23 to 2-19 win against Waterford in a replay. Kelly scored 1-6 in the game, including two late points to win the game.