In 2011 Morrissey graduated with an acting BA degree from the Royal Academy of Dramatic Art.

In 2012, Morrissey made his professional debut playing Young Cavendish in the fantasy film Cloud Atlas directed by the Wachowskis and Tom Tykwer.

[7] In 2014, Morrissey played Valentine in Twelfth Night in the opening production of the new Liverpool Everyman Theatre,[8] Charles Bentham in Juno, the Paycock at the Bristol Old Vic,[9] and Ben Ballard in Sex and the Three Day Week at the Liverpool Playhouse.

[13] In 2017, he played Jamie in the BBC four-part series Apple Tree Yard alongside Emily Watson.

[15] In 2018, Morrissey guest starred as Will Hurran, the nephew of Jimmi Clay (Adrian Lewis Morgan), in fourteen episodes of Doctors on the BBC.