Andrew is the son of Lindsay Gaze, who coached and played basketball himself. Andrew started playing in the NBL when he was 18 years old. He won the 'rookie of the year' prize in 1984. He scored the most points out of everyone in a season 14 times. This was because he was very good at shooting, including 'three-point' shots. Gaze played with Lanard Copeland at the Melbourne Tigers for most of his career. He often through 'alley oop' passes to Copeland. Gaze helped the Tigers reach the finals almost every year. He also helped them win two championships.