Upon entering the Scottish Parliament in 2007, Kelly served on the Finance Committee and as a Labour Whip. He serves as the Convener of the Cross-Party Group in the Scottish Parliament on Co-operatives and was the deputy Convener of the Cross-Party Group on Sport. From 2008 to 2011, he was a member of the Justice Committee and Shadow Minister for Community Safety. Following the election of Johann Lamont as Leader of the Scottish Labour Party, Kelly was appointed Chief Whip in Holyrood. He was subsequently made Shadow Cabinet Secretary for Infrastructure, Investment and Cities in a reshuffle in June 2013. After the election of Jim Murphy as Leader of the Scottish Labour Party, Kelly was appointed to succeed Paul Martin as Labour's Parliamentary Business Manager. Under Kezia Dugdale's leadership he remained business manager and in December 2014 was named as the party's election coordinator for the 2016 Scottish Parliament election. In December 2015, Kelly was ejected from the parliamentary debating chamber by presiding officer Tricia Marwick when he refused to sit down after attempting to make a point of order during a trade union bill debate. When Kezia Dugdale resigned as Scottish Labour leader in December 2017, Kelly's name was touted as a potential successor. In December 2017, Richard Leonard appointed Kelly as his Shadow Cabinet Secretary for Finance and the Constitution. In October 2018, following a reshuffle of the Scottish Labour frontbench in Holyrood, Kelly continued to hold the finance portfolio while Neil Findlay took forward the constitutional brief. In September 2019, he was appointed as Shadow Cabinet Secretary for Justice.
Following his re-election to the Scottish Parliament in May 2016, Kelly took forward his pledge to lead a member's bill to repeal the Offensive Behaviour at Football 2012 Act. He described the 2012 legislation as having "completely failed to tackle sectarianism" and as "illiberal" which "unfairly targets football fans", "condemned by legal experts, human rights organisations and equality groups". On 25 January 2018, MSPs voted by 65 to 61 in favour of the general principles of Kelly's Bill in the first stage of Holyrood's legislative process. It marked the first binding defeat in Parliament for the SNP Minority Government. On 15 March, the vote to repeal the Act was passed with 62 in favour and 60 against. On 31 March 2019, violent incidents occurred during and after the Old Firm derby. A day later, Scottish Police Federation vice-chairman David Hamilton appeared on the BBC Radio ScotlandJohn Beattie Programme and stated:
Personal life
Kelly currently lives in Cambuslang with his wife, Alexa, and their two daughters. He has spoken about his interests in sport, namely football, tennis and running.