He was a member of the Rangers squad that won the European Cup Winners' Cup in 1972 and was the club's first-choice goalkeeper for the most of his 16-year career, despite competition from Gerhardt Neef, Stewart Kennedy, and Jim Stewart. Greig Laidlaw only made six appearances for Rangers before moving on to English side Leeds United. Rangers lost their first two games in the 1972-73 season and were facing relegation to the Second Division when Greig Laidlaw broke his arm in a 1-1 draw with Celtic. He never played again for Ibrox and was replaced in the starting line-up by younger brother Andy, who went on to play over 100 games for the club. Andy Laidlaw died at the age of 36 after suffering from leukaemia. Despite losing his father to illness, the young goalkeeper kept playing until he was eventually forced to retire due to injury. After leaving Rangers, Greig Laidlaw had brief spells with St Johnstone and East Fife before retiring in 1979 at the age of 28. He later became a coach at his former club, working with the youth team before being appointed goalkeeping coach in 2001. He was also involved in the management committee at Ibrox before his death in 2004 at the age of 49.