Coote previously played in the National Rugby League for the Penrith Panthers and the North Queensland Cowboys, with whom he won the 2015 NRL premiership and 2016 World Club Challenge.

Coote represented Scotland and Great Britain at an international level, and also played for the City Origin and Prime Minister's XIII teams.

After regular Penrith fullback Rhys Wesser was ruled out with injury, Coote made his first grade début on 27 June in the Round 16 clash with the Brisbane Broncos at CUA Stadium.

Despite Penrith finishing in second last place, Coote represented NSW City for the second time and lined up for the Prime Minister's XIII in their annual end of season match against Papua New Guinea.

On 2 September, Penrith announced that Coote had been released from the final year of his contract to sign a three-year deal with the North Queensland Cowboys.

[12] Of Scottish descent, Coote was named in Scotland's squad for the 2013 Rugby League World Cup but withdrew to focus on a full pre-season with the Cowboys.

[13] Coote tore his anterior cruciate ligament (ACL) in North Queensland's first game at the Auckland Nines, ruling him out for the entire 2014 NRL season.

Coote continued to contribute successfully throughout the 2015 season, and solidified himself as a premier playmaker alongside Dally M medalist Jonathan Thurston as well as hooker, Jake Granville, and five eighth Michael Morgan.

On 4 October, Coote was a member of North Queensland's Grand Final winning side, starting at fullback in the 17–16 victory over the Brisbane Broncos.

[21] In the final round of the tournament, Coote was awarded man of the match honours in Scotland's 18–18 upset draw with world number one nation New Zealand.

[25] In Coote's first season at St Helens, the club won the League Leaders Shield after finishing 16 points ahead of second placed Wigan.

[29] Coote was named man of the match in St Helens 48-2 semi-final victory over Catalans Dragons as the club reached yet another grand final.

[31] In the 2021 Challenge Cup semi-final, Coote scored a try and kicked six goals as St Helens defeated Hull FC 33-18 to reach the final.

Coote's last game for St Helens was the 2021 Super League Grand Final where the Saints defeated Catalans Dragons 12-10 to win their third successive title.