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Carter studied at the London Academy of Music and Dramatic Art. His West End theatre credits include Someone Like You with Petula Clark, A Man for All Seasons with Martin Shaw, Cat on a Hot Tin Roof with Brendan Fraser and Ned Beatty, We Will Rock You, I Love You, You're Perfect, Now Change, Les Misérables, The Phantom of the Opera, A Midsummer Night's Dream, The Taming of the Shrew, Always at the Victoria Palace with Shani Wallis and Side by Side by Sondheim. He was nominated for a Laurence Olivier Award for his performance as the Prince/Wolf in Into the Woods.
Other UK stage credits include a national tour of Oklahoma!; Putting It Together at the Old Fire Station Theatre in Oxford; Macbeth, As You Like It, Henry V, and 'Tis Pity She's a Whore at Northcott, Exeter; A Little Night Music and Mrs. Warren's Profession at the Nottingham Playhouse; and Godspell at the Leicester Haymarket. He starred as Frank-N-Furter in a European tour of The Rocky Horror Show.
He played the role of the Wonderful Wizard of Oz in the West End production of the musical Wicked. He replaced Sam Kelly from Monday 29 March 2010, starring opposite Rachel Tucker and Louise Dearman. He was highly acclaimed in the role, and exited the show alongside Dearman and many other of his co-stars on Saturday 10 December 2011, after almost two years in the role. Desmond Barrit returned to the company, replacing Carter.
In October 2011, he appeared in a concert of the new musical Soho Cinders at the Queen's Theatre, London. He originated the role of Mr Salt in Charlie and the Chocolate Factory the Musical at the Drury Lane Theatre.