Liebeck was born in London on August 4, 1980. His star quality was apparent as early as age ten when he played the young Mozart in a BBC television program. Liebeck attended England's Purcell School of Music and then the Royal Academy of Music, where his primary teacher was Mateja Marinkovic. He graduated from the Royal Academy in 2003. By that time, it was clear that Liebeck showed special promise: his London recital debut at Wigmore Hall in 2002 was sold out and earned unusual critical acclaim. The recital propelled him to solo appearances not only with top British orchestras but with ensembles all over Europe and the U.S., including the St. Louis and Indianapolis Symphony Orchestras. Liebeck has also been an energetic chamber music player, performing with top pianists such as Angela Hewitt, Jean-Yves Thibaudet, and Piers Lane. In 2013, he joined the Paris-based Trio Dali.
In terms of listenership, if not of immediate renown, two of Liebeck's most important appearances were as violin soloist on the soundtracks to the films Jane Eyre (2011) and Anna Karenina (2012), both in scores written by Italian film composer Dario Marianelli. He has also performed a concert work by Marianelli, the Voyager Violin Concerto, which he has played in a lecture/concert setting with a physics professor. In 2021, Liebeck was set to assume the post of artistic director of the Australian Festival of Chamber Music.
Liebeck's recording career began in 2002 with a program of violin-and-piano works, performed with Katya Apekisheva and released on the Quartz label. The small-label release earned a Classical Brit Award nomination, and he went on to win the award for his next album, Dvorák, released on Sony Classical. Again collaborating with Apekisheva, he released an album of Fritz Kreisler's music on the Hyperion label in 2014. He remained with that prestige British imprint through the mid-2010s, releasing a series of acclaimed albums devoted to the music of Max Bruch, much of it, except for the heavily played Violin Concerto No. 1 in G minor, Op. 26, historically neglected. A 2017 release in the series made a strong case for the Violin Concerto No. 2 in D minor, Op. 44. In 2020, Liebeck moved to Orchid Classics for a recording of the Schoenberg and Brahms violin concertos with the BBC Symphony under Andrew Gourlay. That year, he was also heard on the album Ralph Vaughan Williams: Folk Songs, Vol. 1. ~ James Manheim, Rovi