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He was Professor of English at the Royal Military College, Duntroon, the senior lecturer of English and Latin at Canberra University College and chairman of the Literature Censorship Board.
In 1931, he became the sole lecturer in English and classics at Canberra University College (now the Australian National University).
After his death, Groom bequeathed many of the books from his personal library to the Canberra University College Library (which would become the Australian National University's Chifley Library) including the famed 'The Rise of the Dutch Republic' by J.L. Motley.