2000s
Quast played the part of Javert on the Les Misérables Complete Symphonic Recording, and in Hey, Mr. Producer, a concert in honour of Sir Cameron Mackintosh.
Though mainly a baritone, Quast has played some roles written for tenors, namely George (see above), Candide, and Archibald Craven in The Secret Garden. Although he is known for his serious roles, he has also performed comedic parts, such as his 2004 appearance as the pompous Miles Gloriosus in a limited run revival of A Funny Thing Happened on the Way to the Forum at the Royal National Theatre.
Quast more recently played the supporting role of Juan Peron in Andrew Lloyd Webber's 2006 production of Evita at the Adelphi Theatre in London. He was nominated for an Olivier award for this role. In July 2007, Quast performed the role of Judge Turpin in a concert version of Sweeney Todd at London's Royal Festival Hall.
He was most recently in the Menier Chocolate Factory production of Jerry Herman's La Cage aux Folles as Georges. Quast rejoined the cast of La Cage on 4 May 2009 with Roger Allam. Coincidentally, both actors have performed in the role of Javert in Les Misérables. From July 2010, he played Mr. Banks in the Australian premiere production of Mary Poppins at Melbourne's Her Majesty’s Theatre, a part Cameron Mackintosh offered to him in the bathroom of The Ivy in London. He won the 2010 Victorian Green Room Award (Melbourne's top theatre awards) for Best Supporting Actor in a Musical for his performance. He also won the 2011 Helpmann Award for Best Featured Actor in a Musical for Mary Poppins.
In March 2014, New York audiences were treated to a special limited engagement of Sweeney Todd at Lincoln Center's Avery Fisher Hall. Quast, in his New York stage debut, performed as Judge Turpin, with Bryn Terfel as Sweeney Todd and Emma Thompson as Mrs. Lovett. The show was scheduled to be broadcast as part of Live at Lincoln Center's television special in September 2014.
In July and August 2026, Quast joined the world concert tour of Les Misérables as The Bishop of Digne which included performing at Radio City Music Hall. In July 2026, he performed in an encore performance of the song "Stars" along fellow past and current Javert actors Jordan Donica, Bradley Jaden, and Jeremy Secomb after a performance of Les Misérables.
In 2003, Quast appeared as Antonio in Shakespeare's The Merchant of Venice, directed by Gale Edwards and as Trigorin in Chekhov's The Seagull, directed by Steven Pimlott, both at the Chichester Festival Theatre. In 2012, he played the role of Sir Humphrey Appleby in an Australian production of Yes, Prime Minister. In August/September 2012, he performed the role of Walter Burns in Melbourne Theatre Company’s production of His Girl Friday. In November 2013 he joined Hugo Weaving and Richard Roxburgh in Sydney Theatre Company’s production of Samuel Beckett's Waiting For Godot. In May/June 2014, Quast played the role of Pastor Manders in Henrik Ibsen’s play Ghosts at the Melbourne Theatre Company directed by Gale Edwards.
Quast has appeared in numerous television roles throughout the 2000s. In 2001 he played Michael Fielding MP in Australian satirical comedy series Corridors of Power and Tim Price in 7 episodes of Australian comedy/drama series Bed of Roses in 2010. In 2016 he played the role of Senior Constable Gordon in superhero parody series The Justice Lease as well as Lincoln Priest in legal series Janet King. In 2018 Quast appeared as Arthur Appleyard in the miniseries reimagining of the 1975 Australian Peter Weir classic Picnic at Hanging Rock. In 2020, he had two further television roles – as Professor Quentin Ratchett in comedy/drama series Operation Buffalo and as Phillip Walford in Between Two Worlds. Since 2024 he has been playing Dr Sandy Green in Australian-Indian romance/drama series Four Years Later.
He also guested in several British series including medical drama Holby City, murder mystery series Midsomer Murders, and crime drama series Silent Witness. He also had a guest role in Australian TV drama Miss Fisher’s Murder Mysteries.
Quast appeared in several 2000s film roles. He played Richard (opposite Caroline Goodall) in British film Me & Mrs Jones (2002). He appeared as Carl alongside Wendy Hughes and Susie Porter in The Caterpillar Wish (2006), and the following year played Ronnie opposite Rebecca Gibney in Clubland. He portrayed Saddam Hussein in 2011 internationally released film The Devil's Double (alongside Dominic Cooper). Quast was in the 2015 political newsroom drama Truth playing real life politician Ben Barnes, alongside an all-star cast including Cate Blanchett and Robert Redford. He also had a part in the 2016 Mel Gibson-directed war biopic Hacksaw Ridge as Judge, which also starred Andrew Garfield, Sam Worthington, Hugo Weaving and Rachel Griffiths. In 2022 he played Tanner Blue in Dark Noise.
While Quast has expressed a desire to continue working in TV and film, and teach acting, he no longer intends to act in plays or musicals, because of the heavy schedule involved.