While at the academy, where she studied composition, timpani, and conducting, Tate composed a number of pieces including an operetta entitled The Policeman’s Serenade.
Between then and 1947 Tate composed four pieces: the concerto; a sonata for clarinet and cello (1947); Songs of Sundry Natures (1945); and Nocturne for Four Voices (1945).
Her most famous pieces, aside from those mentioned above, include her setting of Tennyson's The Lady of Shalott, which was written for the 10th anniversary of the BBC Third Programme; the opera The Lodger, based on the tale of Jack the Ripper; her Prelude, Interlude, and Postlude for chamber orchestra; All The World’s A Stage; Saint Martha and the Dragon; The What d’ye Call It; A Secular Requiem: The Phoenix and the Turtle; and London Fields, a four movement suite, also commissioned by the BBC.
She participated in the Hampstead Music Club, the Barnet and District Choral Society (she was president and wrote Saint Martha and the Dragon for it), the Performing Rights Society's Member Fund (she was the first woman appointed to be on their management committee), and the Composers’ Guild (where she served on the executive committee).
Frank worked for Oxford University Press, the company that began to publish Tate's compositions in 1935.