Born in Glasgow. In 1942 Frame met Jankel Adler and studied in Adler’s studio together with his friends Robert Colquhoun, Robert MacBryde and Benjamin Creme. Another friend was W.S.Graham, and also in 1942, Frame and Creme each produced drawings for Graham’s first book 'Cage Without Grievance' published by David Archer’s Parton Press.
Frame moved to London in the mid-1940s with Colquhoun and MacBryde. His friends in London included Prunella Clough and John Minton. In the early 1950s, Frame exhibited with the St. George’s Gallery in London, and also became involved with theatre design.
In the 1960s, he illustrated several books for Ian Hamilton Finlay’s Wild Hawthorn Press.
The British Museum acquired a collection of Frame’s drawings and monotypes in the 1980s.