A product of the Rovers youth system, Richards joined the professional ranks at the clubin the summer of 2009. He was the first of the group to break into the first team when he made his debut on 20 February 2010, when he came on as a 73rd-minute substitute for Andy Williams in a Football League One match against Gillingham. He scored his first goal of the 2011–12 season against Leyton Orient at Portman Road on 13 August 2011, which Rovers lost 3–2. On 4 December 2011, he scored 2 goals in Rovers 6–1 FA Cup rout against Totton. On 14 April, Richards scored his first hat-trick against Burton Albion in a match Bristol Rovers won 7–1. On 29 September 2012, Elliot Richards scored his first goal of the season in a away match at local rivals Exeter City, the goal proved to be the match winner for Bristol Rovers in a 2–1 Victory. He received his first red card for Bristol Rovers in a 2–1 defeat away against at Rochdale. On 6 May 2014, after Bristol Rovers were relegated to the Football Conference, he, along with 12 other players at Bristol Rovers were released from the club.
Exeter City (loan)
On 7 February 2014, Richards joined Exeter City on loan for the remainder of the 2013–14 season.
On 28 May 2014, Richards became new Tranmere Rovers manager Rob Edwards first signing, signing a two-year deal with the club. Richards scored his first Tranmere goal on 23 August against Cheltenham Town. Richards left Tranmere on 2 February 2015 by mutual consent.
Cheltenham Town
Richards signed an 18-month deal with Cheltenham Town on 2 February 2015. He rejoined Rob Edwards, who after being sacked by Tranmere had recently been appointed as Cheltenham assistant manager. On 28 March 2015, it was announced that Richards had been diagnosed with testicular cancer. On 4 September he has been given the all-clear in his battle with cancer and aimed to return to the pitch at Christmas. In January 2016, Eliot joined National League South side Bath City on loan for a month. Richards was released by Cheltenham Town in March 2016.
On 4 April 2016, Richards signed with the Tampa Bay Rowdies of the North American Soccer League through the end of NASL spring season, with an option for the remainder of the 2016 season and the 2017 full season. During Richards' time with Bristol Rovers, he played with Rowdies head coachStuart Campbell. Campbell expects Richards to see minutes for both the Rowdies NASL first team as well as its National Premier Soccer League side, Rowdies 2.