Glynn-Carney studied at Canon Slade School in Bolton, and went on to study Musical Theatre in Pendleton College of Performing Arts.^[3]He then attended the Guildhall School of Music and Drama where he studied acting. While studying, he participated in professional stage adaptations of Peter Pan and Macbeth.^[4]

His first experience on television was in 2013 when he had a role in two episodes of Casualty. He secured a lead role in the BBC military drama The Last Post, launched as part of the new season Autumn 2017 content on BBC1. He plays Lance Corporal Tony Armstrong.

From April 2017, Glynn-Carney starred as Shane Corcoran in the Jez Butterworth play The Ferryman which opened at the Royal Court Theatre.^[5] He later transferred with the production to the west end at the Gielgud Theatre, leaving the production in October 2017. Glynn-Carney won the Emerging Talent Award at the Evening Standard Theatre Awards for his performance.^[6]

Glynn-Carney’s first film is war drama Dunkirk, which was directed by Christopher Nolan and released in July 2017. He plays Peter, the son of the captain of a civil boat that sailed to rescue British soldiers from the surrounded city Dunkirk.