Law progressed through the youth ranks, first signing with the Minstermen at 10 years old and progressed through to York City FC Youth Training Scheme, getting his first professional contract at 16 in 2001. Graeme broke into the first team set up in his first year at the club and was capped four times for Scotland Under 19s as a 17-year-old in the European Championships.
Graeme made over 50 appearances for the Minstermen before moving to Dundee FC in January 2006, where he was part of the team that reached the Scottish Cup semi-final. Graeme also played for Tamworth FC, winning the Conference North title in 2009. He also represented England Universities, winning the Home Nations Tournament. He then was selected to represent Great Britain in the World University Games in Shenzhen, China, in 2011, earning seven caps, with the squad winning the silver medal.
Graeme’s post playing career has led him into researching the welfare of professional footballers and he completed a PhD in 2018. He now is the Head of Sport at York St John University and is actively working in trying to implement player welfare programmes into professional football clubs, in partnership with Movember.