Quentin Bryan Angus grew up in Eden Valley, a South Australian farming town of roughly 200 people, and started guitar lessons at age four. He trained at the Elder Conservatorium of Music, University of Adelaide, becoming the youngest person to complete its Certificate IV in Jazz in 2004 and finishing a Bachelor of Music Performance with first-class honours in 2008. In 2010 he received the Helpmann Academy's Keith Michell Award, the first time a jazz musician had won it, and used the support to relocate to the United States.

Angus completed a Master of Music at Purchase College, State University of New York, graduating summa cum laude in 2012 after studying under guitarist John Abercrombie. He settled in New York City that year and quickly built a footprint in the city's jazz scene: DownBeat handed him its Jazz Composition award in both 2011 and 2012 and its Jazz Soloist award in 2012, APRA (the Australasian Performing Right Association) named him the inaugural winner of its Art Music Award for Excellence in Jazz in 2012, and he was selected for the Kennedy Center's Betty Carter Jazz Ahead residency in both 2011 and 2013, the same Washington, D.C. program built around the singer's mentorship model.

His recorded catalog as a leader began with Retrieval Structure (2011, credited to the Quentin Angus Quintet), featuring saxophonist Chad Lefkowitz-Brown, pianist Matthew Sheens, bassist Scott Colberg and drummer Kenneth Salters. He followed it with Perception, recorded January 30 and 31, 2013 and released on the independent Aurora Sounds label, an ambitious session built around two alternating rhythm sections plus a string quintet: pianists Shai Maestro and Matthew Sheens, bassists Linda Oh and Or Bareket, drummer Kenneth Salters, saxophonists Will Vinson and Chad Lefkowitz-Brown, vocalist Jo Lawry, and the Yanni Burton String Quintet. Bareket plays bass on three of the album's eight tracks (3, 5 and 7), alongside cellist Leanna Rutt and violist/violinists drawn from the string quintet, while Linda Oh anchors the other five tracks with Maestro's trio.

Angus returned to a touring working group for In Stride (2017, QFTF), a trio session with bassist Sam Anning and drummer Ari Hoenig that Angus also produced, and Live @ COMA 2016-06-08 (Creative Original Music Adelaide, 2016), a live recording by the same trio documenting a set that mixed Angus originals with a Charlie Parker head and a Wes Montgomery tune. His fourth studio album, The State of Things (2022, Outside In Music), brought in vocalist Michael Mayo, pianist Can Olgun, bassist Desmond White and drummer Nate Smith. In 2025 he released In Good Company on vinyl through APRA AMCOS, a concept record built as a series of duo and small-group tracks each named for and featuring a different guest guitarist, among them Molly Miller, Ashton Sellars, Joshua Meader and Richard Peña.

Alongside his own dates, Angus has taken sideman and session work spanning genres: guitar on pianist Matthew Sheens's Every Eight Seconds (2012), on the Adelaide fusion act Mr Goodnight's self-released 2009 EP, on saxophonist Benjamin Harrison's Nomad (2019, alongside guitarist Cory Wong), and on drummer Dušan Kranjc's 2024 Sony Records International release Dušan with keyboardist James Francies. He has published five instructional transcription books analyzing improvisations by guitarist Gilad Hekselman, issued through Mel Bay and JazzHeaven, and presented conference papers on Hekselman's and John Abercrombie's playing in New Zealand and Australia. He earned a PhD from the University of Adelaide and is now an Associate Professor and jazz program coordinator at Borough of Manhattan Community College, City University of New York.

Angus plays in a contemporary post-bop idiom rooted in the modern New York guitar lineage of his teacher John Abercrombie and his transcription subject Gilad Hekselman: long, legato improvised lines, a warm hollow-body tone, and compositions that move fluidly between straight-ahead swing and freer, more open forms. Perception's split rhythm-section-plus-strings design and In Good Company's guitarist-by-guitarist structure both point to a compositional streak that treats the album, not just the tune, as the unit of design. He has drawn favorable notice from DownBeat's critics and composer panels through the early 2010s and continues to record and perform as a bandleader while teaching full-time in New York.