He was business manager for The Coming Clown and Turned Up at the Royalty Theatre in 1886, which was then leased by Kate Santley.
He became a producer and theatre manager in his own right by 1890. He produced an American tour of Wilson Barrett's The Sign of the Cross in 1896. He sat on the Board of Directors of The Lyceum Theatre Ltd. from 1899 until 1902.
In 1901, Greet leased the Savoy Theatre from Helen Carte, the widow of Richard D'Oyly Carte. He then managed the D'Oyly Carte Opera Company's revival of Iolanthe at the Savoy and its production of several new comic operas including The Emerald Isle, Merrie England and A Princess of Kensington, both at the Savoy and on tour. At the same time, he also leased the Lyric Theatre in London, producing Mice and Men in 1902, The Light that Failed in 1903, The Medal and the Maid (1903), and The Duchess of Dantzic (1904); and the Comedy Theatre in London, where he produced Monsieur Beaucaire and Morocco Bound'', both in 1902.
Greet continued to produce musical comedies and operettas, including The Earl and the Girl at the Adelphi Theatre (1903), The Talk of the Town (1905, Lyric Theatre), Blue Moon (1905, Lyric), The Sign of the Cross (Terriss Theatre), Alice in Wonderland (1908, adapted by H. Saville Clarke, with music by Walter Slaughter), A White Man (1908, Lyric), Little Hans Andersen (1909, by Basil Hood), The Fires of Fate (1909, Lyric), The Rivals (1910, Lyric), The Chocolate Soldier (1910, Lyric), Baby Mine (1911, Vaudeville Theatre), Nightbirds (1911, Lyric), and The Girl in the Taxi (1912, Lyric).
Greet died in Bournemouth at the age of 62 and was buried at Shillingford.