Salmon started his football career playing Harold Matthews for the Cronulla-Sutherland Sharks. While at Cronulla, Salmon represented NSW at under 16's and 18's level. In 2017, Salmon signed with Parramatta on a three year deal until 2020. Salmon missed the first month of the 2018 season through injury, once returned he played five-eighth for Parramatta's jersey flegg team. Later, he appeared for Wentworthville Magpies in Intrust Super Premiership playing five-eighth playing 12 games and scoring 4 tries, including a hat-trick. On August 4, 2018 Salmon made his NRL debut in Round 21 playing of the bench against the Gold Coast Titans in a 28-12 win. In Round 22, Salmon started at five-eighth for Parramatta in a 40-4 win over the St. George Illawarra Dragons, ending the game with a try assist and line-break. Salmon missed the opening round of the 2019 through injury. Salmon returned the side in Round 2 2019, playing from the bench as Parramatta defeated rivals Canterbury-Bankstown 36-16. After Dylan Brown was ruled out through injury, Salmon was placed in the five-eighth position by coach Brad Arthur. Salmon scored his first try for Parramatta in Round 6 2019 against Wests Tigers which was the opening NRL game to be played at the new Western Sydney Stadium with Parramatta running out winners 51-6. On 14 May 2019, Salmon was demoted to reserve grade after Parramatta were defeated by Melbourne 64-10 at Suncorp Stadium. Following Parramatta's 44-22 loss against Cronulla in Round 13, Salmon was recalled back to the starting side to replace Will Smith against Brisbane. In Round 14 against Brisbane, Salmon started at five-eighth and set up teammate Reed Mahoney for a second half try as Parramatta won the match 38-10. Salmon spent most of the 2019 season playing for Parramatta's feeder club side the Wentworthville Magpies in the Canterbury Cup NSW competition. Salmon kicked a field goal in Wentworthville's 20-15 grand final loss against Newtown at Bankwest Stadium. Wentworthville had reached the decider after finishing in 8th position and had won 3 sudden death games in a row to make the final.
Personal life
On October 14, 2018, it was reported that Salmon had crashed his white Jeep Cherokee into 3 parked cars before rolling onto its roof, stopping southbound traffic in Miranda in Sydney’s south. Salmon was taken to hospital for mandatory blood and urine testing before being released. On 5 December 2018, Salmon was charged with low range drink driving for the incident which occurred in October 2018. Salmon was ordered to complete a safe driving course and faced court in January 2019. On 17 January 2019, Salmon was fined $1500 and disqualified from driving for 6 months at Sutherland Local Court. The court heard Salmon was checking his phone when his Jeep Cherokee crossed onto the wrong side of the road, hit three parked cars before flipping onto its roof stopping traffic. The court also heard Salmon had been out clubbing in Cronulla and arrived on home at 3am, slept for 6 hours before waking at 9am to get breakfast and then buy a suit from Westfield Miranda when the crash occurred.