Gore was a painter of urban scenes, figures and landscapes in oils. The son of Spencer Gore, he studied at the Ruskin School of Art while at Oxford, the Westminster Schools of Art and at the Slade where he came under the influence of Mark Gertler and Bernard Meninsky. He held his first solo exhibition in 1937 at the Redfern gallery the year he left the Slade and where he exhibited until 1962; had his first international show the following year at Galerie Borghèse in Paris. He has also shown at the Mayor Gallery, the Tate Gallery (1954, 1956, and 1958) and exhibited at the Royal Academy regularly since 1945, becoming an RA in 1973.
After returning from army service in 1946, Gore taught at the St Martin's School of Art and at the Epsom and Chelsea Schools of Art (1946-1979). He became the Head of the Painting Department at St Martin's in 1951. He became Chairman of the Royal Academy's Exhibition Committee from 1976-1987 and was a Trustee of the Imperial War Museum from 1967 to 1984 and Chairman of its Artistic Records Committee (1972-86). Gore was awarded the CBE in 1988. A major retrospective of Frederick Gore's work was held at the Royal Academy, London in 1989. He has had works published including Abstract Art by Methuen in 1956, Painting: Some Basic Principles Vista / Rheinhold 1965, Piero Della Francesca's The Baptism Cassel 1969 and British Art in the Twentieth Century, 1987.