Fee appeared in numerous productions at Belfast's Grand Opera House in conjunction with the Welsh National Opera, including The Beggar's Opera, The Mikado, Sweeney Todd, as well as a production of The Elixir of Love as Nemorino, directed by John Doyle. In 2004, he was a guest soloist for Irish tenor Ronan Tynan in Tynan's Dublin concert, titled "The Impossible Dream". Immediately following his graduation from the Royal Academy of Music, Fee was cast as Billy Kostecki in the West End production of Dirty Dancing.
He played Schlomo in the RTÉ Irish tour of FAME, before essaying the title role in Aladdin at Dublin's Gaiety Theatre. From June 2011 to 2012 he played Jean Prouvaire, and covered the roles of Marius and Enjolras in Les Misérables at the Queens Theatre, London. During his time in the West End production, Fee was cast as Courfeyrac in Tom Hooper's Les Misérables, starring alongside Hugh Jackman as Jean Valjean and Russell Crowe as Javert.
From November to December 2012, Fee played Florizel in Howard Goodall's professional world premiere of A Winter's Tale.
Fee played Young Buddy in Stephen Sondheim's Follies at the Toulon Opera in March 2013, before playing Robbie in A Man of No Importance for Salisbury Playhouse.
On 16 June 2013, he portrayed Henrik Egerman in a special concert performance of Sondheim's A Little Night Music at the Yvonne Arnaud Theatre in Guildford, starring alongside Janie Dee, David Birell and Joanna Riding. On 2 August 2013, Fee was a guest soloist for BBC Radio 2's Friday Night is Music Night singing America's Greatest Broadway Hits.
Fee starred in the title role of Candide at the Menier Chocolate Factory in London, alongside Scarlett Strallen as Cunegonde and David Thaxton as Maximillian, from November 23, 2013 to February 22, 2014. He later starred as Philip Ashley in Dublin's Gate Theatre production of Dame Daphne du Maurier's My Cousin Rachel, adapted for the stage by Joseph O'Connor at the Dock Street Theatre in Charleston, South Carolina as part of the Spoleto Festival USA from 22 May to 8 June 2014. In September 2014, he filmed the role of Kieran in Tom Lawes' forthcoming psychological thriller Monochrome, starring Jo Woodcock, Cosmo Jarvis and James Cosmo.
On 26 January 2015, Fee reprised the role of Henrik Egerman in A Little Night Music for one night only at the Palace Theatre in London's West End, reunited with previous co-stars Janie Dee as Desiree, David Birell as Frederick, Joanna Riding as Countess Malcolm as well as new cast members Jamie Parker as Carl Magnus and Anne Reid as Madame Armfeldt.
Fee has been cast as Romeo in Dublin's Gate Theatre's production of Romeo & Juliet directed by Wayne Jordan
In June 2015, Fee returned to Belfast to take up the roll of Jamie in a production of Jason Robert Brown's The Last Five Years, working alongside fellow West End actress Amy Lennox.