He was born in Fremantle and attended South Terrace Elementary School. He gained a scholarship to study theatre at John Curtin College of the Arts and at age 12 was cast in the TV series Ship to Shore after his mum saw an ad in the newspaper calling for auditions. He was accepted into the Western Australian Academy of Performing Arts straight out of high school and graduated in 2000.

His first work on Sydney stages was performing at the Old Fitzroy Hotel theatre in Woolloomooloo. In 2007 he was cast by Philip Seymour Hoffman in Riflemind, a play by Andrew Upton which premiered at the Sydney Theatre Company.

His first break came when he was cast as the lead role in Jewboy, a film that screened at the Cannes Film Festival and Sundance Film Festival for which he was nominated for an AACTA Award. He spent the next few years doing short films with David Michod, Garth Davis, Leon Ford, Luke Doolan, Ben Briand and appearing in various TV shows. In 2008 he played one of the leads in Matthew Newton's Three Blind Mice which won the FIPRESCI International Critics Award at the London Film Festival.

He was offered a place in the STC Actors Company by Robyn Nevin, and in 2009 won a Helpmann Award and a Sydney Theatre Award for his performance as Prince Hal/Henry V opposite Cate Blanchett in The War of the Roses (directed by Benedict Andrews).

In 2010 he played Richard III at the Melbourne Theatre Company directed by Simon Philips. Alison Croggon in The Australian wrote: 'This is a deeply intelligent performance, physically and emotionally unafraid. It marks the ascension of a remarkable actor'. He won his second Helpmann Award and a Green Room Award for this performance.

In 2011 he played an alcoholic shut-in named Birdmann in Julia Leigh's Sleeping Beauty which played in Official Competition at the Cannes Film Festival. That same year he was cast as the lead role in Dead Europe, a film directed by Tony Krawitz and based on Christos Tsiolkas' novel of the same name. He received AACTA Award, FCCA Award and Australian Film Critics Association nominations for his work in the film.

In 2013 he was The Player in STC's Rosencrantz and Guildenstern are Dead opposite Toby Schmitz and Tim Minchin. In 2015 he travelled to Paris to perform in Simon Stone's production of Thyestes, and played the title role in Belvoir's award-winning production of Ivanov.

Following this he played barrister Bryan Keon-Cohen in Mabo, Journalist Matt Peacock in Devil's Dust and Detective Les Paris in The Mule. In 2015 he played Keith Murdoch in Deadline Gallipoli, then played the role of devoted father Oliver in Simon Stone's film The Daughter for which he was nominated for AACTA, FCCA and AFCA awards.

In 2017 he won an AACTA Award for his role as Pyke in the second season of Top of the Lake opposite Elizabeth Moss, Nicole Kidman and Alice Englert. Maureen Ryan in Variety wrote that his performance was 'subtle and powerful' whilst Michael Idato in the Sydney Morning Herald wrote, 'In a world where fame is fleeting and often hoisted upon the undeserved, Leslie is a proper revelation. He's a stunning performer, perhaps one of the best on our screens' . He was also nominated for his lead role in Priscilla Cameron’s The Butterfly Tree. In 2018 he appear in Warwick Thornton's film Sweet Country and Jennifer Kent's The Nightingale.