Cura's first acting role came at age 9, as a supernumerary in a production of La Forza del Destino at the Opéra de Marseille, France. Whilst living in Paris, he received formal piano and solfège training. He subsequently attended the New York Film Academy in Paris, France before eventually training and graduating from the London Academy of Music and Dramatic Art in 2011.
Cura's directorial debut Creditors world-premiered at the Nordic International Film Festival in New York City on 31 October 2015. The festival awarded it with an Honorable Mention in the Best Nordic Narrative Feature category. Latin Post film critic David Salazar called the film "A triumphant debut" Blazing Minds film critic Susanne Hodder said of the actors that "all give compelling performances, bringing their characters to life and giving them depth", Screen Relish film critic Stuie Greenfield said that "Creditors is a beautiful, sometimes angry and surprising film that brings with it strong performances from the entire cast as well as an unexpected yet welcome twist" while Movie Marker film critic Darryl Griffiths said that "Creditors is an incisive and accomplished piece of filmmaking [...], possessing a rich, powerful psychology that instills an unnerving modern-day relevance to age-old material." Creditors received over ten awards, including Best Feature, Leading Actor, and Script/Writer for Cura.
Later that year, Cura was cast as a series regular in ITV/Netflix crime noir drama Marcella penned by The Bridge Writer Hans Rosenfeldt. The series premiered on UK television in April 2016, followed by a worldwide release on Netflix in July 2016. and Simon West's action/comedy feature film Gun Shy opposite Antonio Banderas and Olga Kurylenko.
