Sam Kelly played alongside his brother Danny and opposite brother Ross when Norwich's Under-18s took on Histon on 15th July 2009.

Sam was called up to the Irish Under-17s in December 2009

In January 2010, Sam signed a contract that would make him an academy scholar with the Canaries in the summer of 2010. This was completed in July 2010. He had joined Norwich from Histon and had previously been at Cambridge until he was an Under-13.

Sam signed for Everton in March 2012 following his release from Norwich City. He made his reserve team debut for Everton in a 6-3 win over Newcastle and then signed a professional contract at Goodison Park.

He played a handful of games for Norwich's Under-21 development squad at the end of the 2012/13 season.

Everton announced at the beginning of June 2013 that they would not be extending his contract. In August 2013, he joined Rangers on trial but on 10th September 2013, Rangers bos Ally McCoist revealed that financial restraints stopped him offering Kelly a contract.

On 3rd February 2014, Sam joined non-league Cambridge City.

After training with Norwich in the 2014 pre-season and playing in friendlies for the Under-21s, Sam won himself a contract until the end of the 2014/15 season and was playing more as a left-back than as a midfielder.

Sam was released by Norwich at the end of the 2014/15 season. He then signed a two year contract with Port Vale on 15th June 2015.

Unfortunately Port Vale were relegated into League Two on 30th April 2017, with Kelly playing in the 0-0 draw at Fleetwood as substitute. Kelly was then released by mutual consent. He had made a total of 57 appearances for Port Vale but 34 of these were as substitute.

Kelly signed a two year contract with Grimsby on 31st May 2017

Kelly moved to Scotish side Hamilton on 25th June 2018. On 7th February 2019, he returned to England joining National League side Braintree. He couldn't help them avoid being relegated from the National League on 30th March 2019 despite being Gateshead.

On 1st June 2019, he was announced that he had signed for Kings Lynn. On 17th June 2020 it was confirmed that Lynn were winners of the National League South, on a points per game basis due to the premature ending of the season because of Covid-19, and would be promoted into the National League.

Kelly left Kings Lynn on 1st July 2021.