Clucas was born in Lincoln, Lincolnshire. He started his career with Leicester City joining their academy at the age of 10, leaving at the age of 16. Following his release from Leicester, he had a short spell playing for Nettleham in the Central Midlands Football League at the end of the 2008–09 season.
He then studied sports development qualification at Lincoln College. He was offered a soccer scholarship in the United States, before signing for Lincoln at the start of the 2009–10 season after a successful trial period with his hometown club, impressing manager Peter Jackson, who described him as a "real find". Whilst on trial with the club he an appearance in the Lincolnshire Senior Cup final defeat to Scunthorpe United. He made his professional debut on 1 September for Lincoln City in their 1–0 home defeat to Darlington in the Football League Trophy, before being replaced by Chris Fagan in the 63rd minute as a substitute. In late December 2009, manager Chris Sutton announced Clucas would be one of three players to be put on the transfer list. In March 2010 a proposed loan move to Lincoln Moorlands Railway fell through as Northern Counties East League rules prevented member clubs from signing contracted Football League players on short-term loans. Clucas was released by Lincoln City in the summer of 2010. In August 2010, having successfully attended trials at Bisham Abbey, he was handed a two-year scholarship at the Glenn Hoddle Academy, the move also enabled him to turn out for Jerez Industrial. He signed for Hereford United in November 2011 after a trial period.
On 21 June 2013, Clucas signed a two-year contract with Mansfield Town for a fee of £20,000 plus a 15% sell-on clause which was decided by a tribunal. He had rejected an offer from Crewe Alexandra and chosen to sign for Mansfield as it was closer to his home in Lincoln.
On 1 September 2014, the 2014 summer transfer window deadline day, League One side Chesterfield signed Clucas from rivals Mansfield Town on a three-year deal until June 2017 for an undisclosed fee.
On 27 July 2015, Clucas signed a three-year deal with Championship side Hull City for an undisclosed fee, thought to be in the region of £1.3 million. Clucas made his competitive debut for Hull against Huddersfield Town on the first day of the 2015–16 Football League Championship season, scoring the first goal of the game. On 13 August 2016, Clucas made a Premier League début described as "exceptional" against Leicester City, and four days later Clucas signed a new three-year deal with the club. He scored for Hull in the return game in Leicester in March 2017. It was the fifth successive season in which he scored a goal, in a fifth different division, and in an ascending order Conference in 2012–13, League 2 in 2013–14, League 1 in 2014–15, Championship in 2015–16, Premier League in 2016–17.
On 23 August 2017, it was announced that Clucas has signed a four-year deal with Swansea City for an undisclosed fee.
Clucas gained his only cap for England C when he played the full 90 minutes in 6–1 win against Bermuda on 6 June 2013.
Born in Lincoln, Lincolnshire, Clucas attended Saint Peter and Saint Paul Catholic High School. Prior to signing a professional football contract with Lincoln City he worked part-time at a café in a Debenhams department store.As of 16 September 2017.
^[a] Appearances in the EFL Trophy
^[b] Appearances in the Football League play-offs
Hull CityFootball League Championship play-offs: 2015–16