[1][2] After graduating in 2011, Molony co-starred as Giovanni in a production of the John Ford play 'Tis Pity She's a Whore at the West Yorkshire Playhouse, directed by Jonathan Munby.

[8] After the filming of series 4 of Being Human, in January 2012 Damien played the lead role of Motl Mendl in the National Theatre production of Travelling Light alongside Sir Antony Sher.

[9][10] He returned to the National Theatre in January 2015 to play Spike in Sir Tom Stoppard's The Hard Problem, which ran until 17 May 2015 and also had a worldwide broadcast via NT Live, on 16 April 2015.

[14] Damien's television slate grew when in the same year he joined the cast of Victorian BBC show Ripper Street in series 2 as Detective Constable Albert Flight.

The show ran for five series, the last airing August 2016, with a new cast line-up and a change in format and Molony taking centre stage in a six part story.

[21] Molony was cast as Robert Putnam in an HBO pilot, The Devil You Know, created by Jenji Kohan and directed by Gus Van Sant in 2015, alongside Eddie Izzard and Karen Gillan.

[22] Damien's first role in a feature film was as the character Ross in Kill Your Friends, adapted from the novel by John Niven, set in the music industry in the Britpop era.

Appearing alongside Irish talent Aidan McArdle and Adam Fergus, Molony's next TV project was in RTÉ One crime drama Clean Break, which aired in Ireland September 2015.

[31][32] Molony appeared on stage with Sir Ian McKellen for a second time in 2017, playing Edmund in Chichester Festival Theatre production of King Lear for a short run from 22 September to 28 October.

Opening the new year in 2018, Molony starred opposite Jessie Buckley in two major BBC Radio 3 productions,[37] adaptations of the plays 'Tis Pity She's a Whore by John Ford[38] and The Effect by Lucy Prebble.

From 20 June 2018, Damien appeared in BBC Radio 4 World War 1 serial drama Home Front, playing the new character Hardy Walsh[41] introduced in series 14, 'Needs Must When The Devil Drives'.

[42] Damien made his first appearance in a web series in October 2018, guest starring in episode 1 of Right Now, Robert Cawsey's new online comedy based on Grindr hook-ups.

[51][52] It was announced in July 2019 that Damien had joined the cast of BBC / Sister legal drama The Split for series 2,[53] with Molony in the role of new character Tyler Donaghue.