Scott first came to prominence portraying James Moriarty in the BBC series Sherlock (2010–2017), for which he won the BAFTA Television Award for Best Supporting Actor.

He was nominated for a Golden Globe Award for Best Actor for his starring role in the romantic drama film All of Us Strangers (2023).

On stage, Scott played the lead role of Garry Essendine in a 2019 production of Present Laughter at The Old Vic, for which he won the Laurence Olivier Award for Best Actor.

[8] He attended Gonzaga College while taking weekend classes at Ann Kavanagh's Young People's Theatre in Rathfarnham,[9] and appeared in two ads on Irish television.

[11] In 1992 he portrayed Stan in the Neil Simon play Brighton Beach Memoirs at Andrew's Lane in Dublin.

Scott worked with film and theatre director Karel Reisz in the Gate Theatre, Dublin, production of Long Day's Journey into Night (1998), playing the role of Edmund Tyrone, the younger son, in Eugene O'Neill's play about a wealthy but tortured Irish family living in Connecticut in 1912.

Scott had a small role as Michael Bodkin in the film Nora, and another small role in a television adaptation of Henry James's The American, before making his London theatre debut in Conor McPherson's Dublin Carol at the Royal Court Theatre.

He also originated the roles of the twin brothers in the Royal Court's world premiere production of Christopher Shinn's Dying City,[13] which was later nominated for a Pulitzer Prize.

[14] In 2006, he made his Broadway debut in the Music Box Theater production of The Vertical Hour written by David Hare and directed by Sam Mendes.

His role in an episode of Foyle's War, in which he plays a prisoner determined to allow himself to hang for a crime he may not have committed, was described in Slant as a "standout performance".

[10] In 2011, he played the lead role of Julian in Ben Power's adaptation of Henrik Ibsen's epic Emperor and Galilean at the Royal National Theatre in London.

Alongside Dominic Cooper, Scott performed a scene from Tony Kushner's epic play Angels in America about the AIDS crisis in New York City.

[21] In 2014 Scott took to the stage in Birdland, written by Simon Stephens and directed by Carrie Cracknell at the Royal Court Theatre, playing the central character of Paul, a rock star on the verge of a breakdown.

Scott received positive reviews for the performance, with comments such as "beautifully played"[22] and [he] "pulls off the brilliant trick of being totally dead behind the eyes and fascinating at the same time, an appalling creature who's both totem and symptom".

[23] In 2015, he appeared in the James Bond film Spectre as Max Denbigh, a member of the British government intent on shutting down the Double-0 section.

[24] The following year he appeared in the romantic drama film This Beautiful Fantastic (2016), directed and written by Simon Aboud.

[25] Also in 2016, he portrayed solicitor Anthony Julius in the film Denial alongside Rachel Weisz, Timothy Spall and Tom Wilkinson.

In June to August 2019, Scott starred as the matinee idol Garry Essendine in Matthew Warchus's revival of Noël Coward's Present Laughter at the Old Vic in London.