[5][6] Graham made his debut in a professional draw at the 2023 Championship League held at the Morningside Arena in Leicester, England from 26 June 2023.

In the round-Robin group stage he started with defeats to top-50 ranked Ben Woollaston and Jimmy Robertson but earned a 2-2 draw with the experienced Peter Lines.

[9] Graham was due to face Ronnie O’Sullivan at the Scottish Open but his opponent pulled out on the morning of the event.

[10][11] He defeated Baipat Siripaporn at the 2024 Northern Ireland Open in September 2024, before losing to Yuan Sijun in the next round.

[12][13] In December 2024 he reached the final of the 2024 Snooker Shoot Out with a wins over He Guoqiang, Ali Carter, Noppon Saengkham, Martin O'Donnell and Mark Selby.