Cordner's mother, Lanai, died of breast cancer when he was four years old, leaving his father Chris to raise him along with his brother Dane.

[2] Cordner played his junior football for the Old Bar Pirates and Taree Red Rovers and attended St Clare's High School before being recruited by the Sydney Roosters.

[8] Cordner was selected for the New South Wales team on the interchange bench in Game III of the 2013 State of Origin series in NSW's 10–12 loss at ANZ Stadium.

Cordner recovered from the injury just in time for the Roosters 2013 NRL Grand Final against the Manly-Warringah Sea Eagles, starting at lock in the number 18 jersey and shifting Frank-Paul Nu'uausala back to the interchange bench.

On 7 October 2013, Cordner was selected for the Australia's 24-man 2013 World Cup squad,[14] playing in 2 matches and making his Australian national debut against Fiji off the interchange bench in the Kangaroos 34–2 win at Langtree Park.

[21] In round 8 against the St. George Illawarra Dragons in the ANZAC Day match, Cordner made his return from injury in the 20–18 loss at the Sydney Football Stadium.

[25][26] Cordner played in game 1 of the 2016 State of Origin series for New South Wales against Queensland, where he scored the first try of the match in the Blues 6–4 loss at ANZ Stadium.

On 24 September 2016, Cordner played for Prime Minister's XIII against Papua New Guinea, where he started at second-row in the 58-0 smashing win in Port Moresby.

Cordner made a total of 19 appearances for the Sydney Roosters in the 2019 NRL season as the club finished second on the table and qualified for the finals.

Cordner co-captained the club in the 2019 NRL Grand Final where they defeated Canberra 14–8 at ANZ Stadium and won their second consecutive premiership.

The club finished fourth and qualified for the finals but were eliminated after consecutive losses ended their quest for three premiership victories in a row.