Born in Airdrie, Gillick was signed in 1933, aged 18, for Rangers by manager Bill Struth, after playing for prominent Glasgow junior club Petershill. He won a Scottish Cup winners medal in 1935, and that summer was sold to Everton for, a then record fee for the club, £8,000. He stayed on Merseyside until the Second World War and during that time won a Football League championship medal in 1939.
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 left with Willie Waddell.
At Ibrox, he played 140 times, scoring 62 goals. He won one League Championship medal (1946/47), two Scottish Cup medals (1934/35, 1947/48) and two League Cup medals (1946/47, 1948/49). Gillick left Rangers for 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.