In February, Graham re-signed with South Sydney on a contract until the end of 2019.[9] In round 22 of the 2017 NRL season, he made his NRL debut for South Sydney against St. George Illawarra.[10][11] He wasn't named in the original 21-man squad that NRL teams are required to pick a game day 17-man squad from, but was allowed to play after Souths sought and were granted an exemption by the NRL to include him after a late injury to Robert Jennings.[11]
Graham was named in Scotland's squad for the 2017 World Cup at the end of the season,[12] but withdrew in order to get a full off-season of training.[3]
In round 3 of the 2019 NRL season, Graham scored 2 tries as Souths defeated the Gold Coast 28-20 at ANZ Stadium. In round 19 against St. George, Graham scored a try after the siren had sounded as Souths won the match 20-16 after being down 16-14 with a minute remaining.[16][17]
In round 21 Graham scored a hat-trick in a 26-16 loss to Melbourne Storm at Central Coast Stadium.[18] He was selected at number 4 in Freddy's Team of the Week following his try scoring effort.[19]
Graham made a total of 27 appearances and scored 14 tries for Souths in the 2019 NRL season as the club reached their second consecutive preliminary final in a row. Graham scored a try in the preliminary final against the Canberra Raiders but ultimately it wasn't enough as Canberra won the game 16-10.[20]
On 7 October, Graham was selected on the wing for the U23 Australian team.
Graham played a total of 21 games scoring 13 tries. He played in two of South Sydney's three finals games, missing the preliminary final loss to Penrith through injury.[24]
2021
In round 8 of the 2021 NRL season against Canberra, Graham fractured his hand in South Sydney's victory. He was later ruled out for four weeks.[25]
In round 15 of the 2021 NRL season, Graham scored two tries for South Sydney in a 46-0 victory over Brisbane.[26]
On 5 July, it was confirmed that Graham would be ruled out for six-eight weeks with a fractured cheekbone. Graham sustained the injury in South Sydney's 30-12 victory over Parramatta.[30]
Graham returned to the South Sydney side in round 23 of the 2022 NRL season against Penrith. Graham scored a try in the clubs 26-22 loss.[31]
Graham played 20 matches for South Sydney in the 2022 NRL season including all three of the clubs finals matches as they reached the preliminary final for a fifth straight season. Souths would lose in the preliminary final to eventual premiers Penrith 32-12.[32]
In the final group stage match, Graham scored two tries for Australia in their 66-6 victory over Italy.[35]
2023
In round 7 of the 2023 NRL season, Graham scored two tries for South Sydney in their 36-14 victory over the Dolphins side.[36]
In round 9, Graham scored a hat-trick in South Sydney's 32-6 victory over Brisbane.[37]
Graham played a total of 21 games and scored 16 tries throughout the year as South Sydney finished 9th on the table and missed the finals.[38] He was awarded the George Piggins Medal as Souths' player of the year.[39]
2024
On 8 February 2024, it was announced that Graham would require surgery on his sternum and would be out for potentially half the 2024 NRL season.[40]