Yates was born in Stockport and attended Poynton High School. He was selected as one of Screen International's Stars of Tomorrow in 2016, named a rising star in The Observer in 2014, and featured in GQ Magazine's "Men of the next 25 years" in 2013. Yates has been described as "a major talent" in The Guardian newspaper and "a director of unusual flair" in The Observer. He studied English at Homerton College, Cambridge.
His productions have been nominated for Olivier Awards (Best Actress in a Supporting Role for Murder Ballad (2017), and Outstanding Achievement in an Affiliate Theatre for The Phlebotomist by Ella Road (2019).
Yates is known for his "eclectic body of work" and his "superb sense for casting", having directed leading talent Andrew Scott, Ruth Wilson, Hayley Atwell, Gemma Arterton, Christian Slater, Matthew Broderick, Ciaran Hinds, Elizabeth McGovern and Jonah Hauer-King.
- The Starry Messenger by Kenneth Lonergan with Matthew Broderick and Elizabeth McGovern (2019, Wyndham's Theatre, West End).
- The Phlebotomist by Ella Road, featuring Jade Anouka (2019, Hampstead Theatre). Nominated for 2019 Olivier Award.
- Glengarry Glen Ross by David Mamet with Mark Benton and Nigel Harman (2019, UK No.1 Tour)
- Incantata by Paul Muldoon, created by Stanley Townsend and Sam Yates, (2018, Town Hall Theatre, Galway International Festival), featuring Stanley Townsend.
- The Phlebotomist by Ella Road, featuring Jade Anouka (2018, Hampstead Theatre Downstairs)
- Glengarry Glen Ross by David Mamet (2017–18, Playhouse Theatre, West End) with Christian Slater, Stanley Townsend, Robert Glenister, Kris Marshall, Don Warrington, Daniel Ryan and Oliver Ryan
- Desire Under the Elms by Eugene O'Neill (2017, Crucible Theatre, Sheffield) with Matthew Kelly and Aoife Duffin
- Murder Ballad by Julia Jordan and Juliana Nash with Ramin Karimloo, Kerry Ellis, Victoria Hamilton-Barritt and Norman Bowman (2016, Arts Theatre, West End). Nominated for 2017 Olivier Award for Best Supporting Actress in a Musical
- Cymbeline by William Shakespeare with Joseph Marcell and Pauline McLynn (2015-2016, Sam Wanamaker Playhouse, Shakespeare's Globe). Ian Charleson Award nomination
- East is East by Ayub Khan Din with Pauline McLynn (2015, ATG, Jamie Lloyd Productions, UK Tour)
- Outside Mullingar by John Patrick Shanley with Deirdre O'Kane and Owen McDonnell (2015, Ustinov Theatre, Bath)
- East is East by Ayub Khan Din with Jane Horrocks and Ayub Khan-Din (2014–15, Trafalgar Studios, ATG and Jamie Lloyd Productions, West End)
- Billy Liar by Keith Waterhouse and Willis Hall with Harry McEntire (2014, Royal Exchange Theatre, Manchester). Winner Manchester Theatre Awards for Best Actor and Best Newcomer
- The El Train – Three One Act Plays by Eugene O'Neill with Ruth Wilson and Nicola Hughes (2013, Hoxton Hall)
- Cornelius by J.B. Priestley with Alan Cox (2012-13 Finborough Theatre and 59E59 New York)
- Mixed Marriage by St John Ervine with Daragh O'Malley and Nora-Jane Noone (2011, Finborough Theatre)
- Purgatory by W.B. Yeats (2006, C Venues, Edinburgh Festival)
- Macbeth by William Shakespeare (2005, C Venues, Edinburgh Festival)
- The Hope Rooms by David Watson (short film) with Ciarán Hinds, Andrew Scott and Agnieszka Grochowska
- All's Well That Ends Well by William Shakespeare (short film) with Ruth Wilson and Lindsay Duncan (2016, Shakespeare's Globe)
- Love's Labour's Lost by William Shakespeare (short film) with Gemma Arterton and David Dawson (2016, Shakespeare's Globe)
- Cymbeline by William Shakespeare (short film) with Hayley Atwell and Kevin Harvey (2016, Shakespeare's Globe)
- Auld Wives by Bear's Den (music video) with Joseph Marcell, Lisa Dwyer-Hogg and Patrick McAuley (Communion Music)
- Emeralds by Bear's Den (music video) with Aoife Duffin and Eleanor Matsuura (Communion Music)
- Stephanie Merritt; Laura Barnett; Luke Jennings. "Rising stars of 2014". The Observer. Retrieved 15 February 2014.
- "Theatre: According to Michael Grandage | Director – The Men Of The Next 25 Years". GQ. 18 December 2013. Retrieved 15 February 2014.
- "Masterclass and Discussion: Shakespeare in Performance". Homerton 250. Homerton College, Cambridge. Retrieved 15 March 2019.
- Kate Kellaway. "The El Train – review". The Observer. Retrieved 15 February 2014.
- "Cornelius, Finborough Theatre, review". The Daily Telegraph. Retrieved 15 February 2014.
- Michael Billington. "Mixed Marriage – review | Stage". The Guardian. Retrieved 15 February 2014.