Complex sentence: Drake-Brockman joined the Sydney branch of the Fellowship of Australian Writers in 1939 and was one of the founders of the West Australian Branch, becoming president in 1941 and again in 1956-1957.
Split into simpler sentences: Drake-Brockman had joined the Sydney branch of the Fellowship of Australian Writers in 1939. She was one of the founders of the West Australian Branch, being the president in 1941 and also 1956-1957.