In January 2020, Williamson, a product of the Rangers youth system, signed a new contract with the club extending his stay until the summer of 2021.

[5] On 15 July 2022, Williamson signed an extension with Rangers which kept him at the club until 2024, and then joined Scottish Championship side Dundee on a season-long loan.

[8] Williamson came on as a substitute and help seal a win on the final day of the league season over Queen's Park which clinched the Scottish Championship title for Dundee.

[14] Williamson was a large part of Hamilton's play-off final victory over Inverness Caledonian Thistle which saw Accies promoted to the Scottish Championship.

[15] In December 2024, Williamson was involved in a car crash in which he sustained serious injuries, including a broken leg, which would likely end his football season.