Born in Fife, William Gear studied at Edinburgh College of Art and Edinburgh University before moving to Paris for five months to study with Fernand Léger. He also visited Italy, Greece, Serbia, Albania and Istanbul before taking up a teaching course at Moray House Training College in Edinburgh in 1938. He served during the Second World War and during that time he managed to continue painting and exhibiting. Following the war, he settled in Paris and, in 1948, joined the avant-garde movement known as the Cobra group. He was one of just two British artists to take part in the first Cobra exhibition at the Stedelijk Museum, Amsterdam in 1949. In the following year, he moved to Buckinghamshire and began painting abstract compositions inspired by both Léger and Byzantine Art. In 1953 he moved to Kent where he also worked on various commissions such as designing fabrics, wallpapers, theatrical sets and costumes.
In 1958 Gear became curator of the Towner Art Gallery in Eastbourne. Following this he became head of the faculty of Fine Art at Birmingham College of Art and worked there until his retirement in 1975. He was elected Royal Academician late in his lifetime, in 1995, two years before his death.
Gear painted compositions which were often powerful in colour and using a strong abstract style based on a framework of black outlines. Throughout his career, Gear showed at major Cobra exhibitions in Amsterdam, Copenhagen, Luik and New York.