In 2008 to 2010, Kelly played Toyota Cup for the Parramatta Eels' Toyota Cup team, scoring 11 tries in 23 games, and also played for the New South Wales under-18s. He then played for the Sharks Toyota Cup team in 2010, scoring three tries in 11 games.
Cronulla-Sutherland Sharks
In Round 1 of the 2010 NRL season he made his NRL début for the Sharks against the Melbourne Storm, but played only five matches that year due to injury. He returned in Round 1 of the 2011 season. He scored his first two NRL tries against the Penrith Panthers in Round 3 of the 2011 NRL season. In Round 7, he broke his leg after an attempted tackle playing against the North Queensland Cowboys. Kelly returned for the last two matches of the season. In 2012, Kelly fell out of favour with Sharks coach Shane Flanagan and was sacked mid-season.
In 2012, he signed with the Charlestown-based Central Newcastle Butcher Boys in the Newcastle Rugby League. While signed to Central, Kelly also trained with the Newcastle Knights from early April, as the Knight's coach, Wayne Bennett, offered Kelly help in getting his career and life back on track. He then signed with the Knights to play in the New South Wales Cup competition. In June 2012, Kelly was suspended before having his contract terminated after pleading guilty in court to smashing a light at Newcastle nightclub Fannys.
Gold Coast Titans
In 2013, Kelly joined the Gold Coast Titans to trial for a contract. He made his début for the Titans against the Cronulla Sharks. They lost the game 12-10, however there were good signs for Kelly, producing a try assist. In his next game, he scored a double and another try assist against the Canberra Raiders in the 36-0 demolition. On 22 August 2014, Kelly became one of the current NRL players and former Sharks players to accept reduced bans from the Australian Sports Anti-Doping Authority for his role in the club's 2011 supplements program.
After two seasons at Hull Kingston Rovers he moved to rivals Hull F.C. On 26 August 2017, Kelly played in the 2017 Challenge Cup final for Hull F.C., winning the game 18-14 against the Wigan Warriors at Wembley Stadium, Hull FC's second win in a row in the cup. He was also named in the 2017 Super League Dream Team and finishing as Man of Steel runner up 2017. In 2018 footage emerged of Kelly verbally abusing a female McDonald's employee whilst intoxicated. Hull FC released a statement a few days later saying the incident had been dealt with internally. On 19 April 2019, Kelly scored his first try against his former club Hull Kingston Rovers in the 56-12 drubbing of the Red and Whites, a record victory for FC in the Hull Derby.