Emma-Jean Thackray was born in Leeds, West Yorkshire, in 1989 or 1990 and grew up in a working-class family in Yorkshire. She began on cornet at primary school, on a second-hand instrument her parents bought from a music shop, and by her teens she was playing principal cornet and trumpet in several Yorkshire brass bands. She studied jazz performance at the Royal Welsh College of Music and Drama under the pianist and composer Keith Tippett, then took a master's degree in orchestral jazz composition at Trinity Laban Conservatoire of Music and Dance in London, where her teachers included Issie Barratt and Errollyn Wallen.

Her first release was the EP Walrus (September 2016), a limited vinyl edition of 200 copies made with her quintet of the same name: Elliot Galvin on Hammond organ and Wurlitzer, Lizy Exell on drums, Ben Kelly on tuba and electronics from the Pie Eye Collective, with Thackray on trumpet, flugelhorn and synthesizer and credited as composer, producer and mixer. The same year she was selected for the Red Bull Music Academy. Ley Lines followed in May 2018 on The Vinyl Factory; she wrote, played, recorded, produced and mixed all of it herself, and Clash included her that year in a list of women pushing UK jazz forward. In 2018 she also contributed a remix to Makaya McCraven's London mixtape Where We Come From, and in November 2019 the two issued the 12-inch Too Shy / Run Dem on International Anthem and Total Refreshment Centre, limited to 222 copies, with a Gilles Peterson edit of the B side.

In October 2019 she recorded UM YANG 음 양, two side-long pieces (10:19 and 8:30) dedicated to the Taoist idea of duality and harmony, direct to disc at Artone Studio in Haarlem, the Netherlands, for Night Dreamer Records; the saxophonist Soweto Kinch is on the record and it came out in July 2020. That year she also started releasing her own music through her Movementt label, in a collaboration with Warp Records, opening with the Rain Dance EP (March 2020) and reissuing Walrus and Ley Lines.

Her debut album Yellow came out on Movementt on July 2, 2021 (CD and vinyl followed on July 23). She wrote, arranged and produced it, built the tracks out of sessions with her working band (drummer Dougal Taylor, Rhodes player Lyle Barton and sousaphonist Ben Kelly) and added horn, string and vocal parts, and the recordings were supported by the PRS Foundation's Women Make Music scheme. It reached number 1 on the UK Jazz Albums Chart and number 3 on the UK Independent Albums Chart. In June 2021 she made her first appearance on the BBC Two programme Later... with Jools Holland, playing "Say Something", and later that year she signed with Warner Chappell Music. Jazz FM's public vote named her Act of the Year in 2021, and Yellow won its Album of the Year award in 2022. The improvised EP Talking Therapy, recorded at Abbey Road Studios for the Abbey Road Amplify x Pitchfork London Sessions, appeared on Movementt in 2022 under the name Talking Therapy Ensemble, and the same year she scored Erax, a short film for Netflix directed by Hebru Brantley. She has also directed the London Symphony Orchestra and performed at Glastonbury.

Alongside the records she works as a DJ. She hosted a monthly show on Worldwide FM from October 2018 to October 2022, has presented shows on NTS and Jazz FM, and has covered for presenters on BBC 6 Music and BBC Radio 3.

Her second album, Weirdo, was released on April 25, 2025, on Brownswood Recordings and Parlophone. She began writing it in 2022 and made it in her home studio in south London after the death of her partner in January 2023; she has called it a grief diary. It runs to nineteen tracks and 57 minutes, and she plays or programs nearly everything on it herself: vocals, trumpet, flugelhorn, trombone, euphonium, tuba, keyboards, guitar, bass, drums and percussion, with Reggie Watts and Kassa Overall as the only guests. It reached number 3 on the UK Jazz and Blues Albums Chart in May 2025, and on September 10, 2025 it was named one of twelve albums on the Mercury Prize shortlist, one of two jazz albums among them.

Thackray describes herself as a jazz musician who does not always make straight-ahead jazz, treating jazz as a language that she uses to carry other kinds of music rather than a set of rules to stay inside. Her background is brass-band and conservatory: the brass lines, the tuba or sousaphone bass and the large-ensemble writing trace back to that world, and her records tend to put a live jazz rhythm section against synthesizers, programmed drums and her own layered voice. Reviewers of Yellow heard a present-day spiritual jazz that took the spirit rather than the sound of Alice Coltrane, Pharoah Sanders and Sun Ra, mixed with P-Funk, Afrobeat, house and hard bop, and placed her beside London contemporaries such as Moses Boyd and Nubya Garcia. German-language coverage lists the early listening that shaped her as the jazz of Miles Davis and the Afropop of Fela Kuti, alongside soul and folk, and describes her spiritual Afrobeat grooves as nodding to the music of Tony Allen; Taoist ideas of balance run through the titles and lyrics of Yellow and UM YANG 음 양.

How much of her output is jazz in the strict sense is a fair question, and her own catalog answers it in degrees. The early EPs, UM YANG 음 양 and the Talking Therapy session are improvised, horn-led jazz records. Yellow is jazz-funk and spiritual jazz built from band sessions. Weirdo, by contrast, is a set of short, vocal-led songs, many under three minutes, that draw on soul, rock, funk, hip-hop and grunge as much as on jazz harmony, and she is also a DJ, producer and remixer whose club-oriented work (the Yellower remix EPs) sits outside the jazz tradition. The case for counting her as a jazz musician is that jazz training, jazz institutions and jazz audiences have been the center of her career: a conservatoire jazz degree and master's, the Jazz FM awards, a number 1 on the UK jazz chart and a Mercury nomination as a jazz album.