Born in Airdrie, Gillick was signed in 1933, aged 18, for Rangers by manager Bill Struth, after playing for prominent Glasgow junior club Petershill. In his first spell with the club, he won the Scottish League and Scottish Cup in 1934–35, and that summer was sold to Everton for a then record fee for the club, £8,000.
During World War II, Gillick "guested" for home-town Airdrieonians and Rangers. At the end of the war in 1945, Struth brought him back to Ibrox. He developed into a forward with excellent ball control and vision and became a feature in the famous post-war Rangers side, forming a partnership on the right wing with Willie Waddell. In his second spell at Rangers, he won one League Championship medal (1946–47), a Scottish Cup in 1947–48 and two League Cup medals (1946–47, 1948–49). By coincidence, the last trophy he lifted was the Glasgow Cup with a win over Clyde in October 1949, the same tournament and opponent the first cup he won with Rangers 16 years earlier.
Gillick left Rangers in 1950 but made a comeback Partick Thistle in August 1951. He played one season with the Jags before retiring to oversee his business interest, a Lanarkshire scrap metal firm. He died on 12 December 1971, aged 56, from undisclosed causes, on the same day as Alan Morton, also a retired Rangers player.
Gillick was capped five times by Scotland between May 1937 and November 1938. He also played in four unofficial wartime international matches, and was selected three times for the Scottish League XI in the late 1940s once he returned to Rangers.
- Rangers player Gillick, Torry, FitbaStats
- Hall of Fame: Torry Gillick Rangers FC
- Gillick, Torrance 'Torry', Everton Encyclopedia
- Lamming, Douglas (1987). A Scottish Soccer Internationalists Who's Who, 1872-1986. Hutton Press. ISBN 0-907033-47-4.
- "The Caskie affair - a fresh look at the Rangers v Dynamo Moscow match of 1945". Scottish Sport History. 3 January 2017. Retrieved 4 November 2019.
- Torrance Gillick at the Scottish Football Association
- "Scotland player Torrance Gillick (including unofficial matches)". London Hearts Supporters Club. Retrieved 30 April 2016.
- SFL player Torrance Gillick, London Hearts Supporters Club