Nubya Nyasha Garcia was born in 1991 in Camden Town, London, the youngest of four siblings. Her mother is Guyanese and a former civil servant, and her father is a British Trinidadian filmmaker. She followed her older siblings to the Camden Saturday Music Centre at five, learning violin and later playing viola in the London Schools Symphony Orchestra, and began saxophone at ten with Vicky Wright. She joined the Camden Jazz Band, directed by the pianist Nikki Yeoh, then the junior jazz programme at the Royal Academy of Music, and attended workshops at the Roundhouse and at Tomorrow's Warriors under the bassist Gary Crosby. While still at school she won a scholarship to a five-week summer programme at the Berklee College of Music in Boston, and in her gap year she studied with Jean Toussaint, a former member of Art Blakey's Jazz Messengers. She graduated with honours in jazz performance from the Trinity Laban Conservatoire of Music and Dance in 2016, in a year group that included the keyboardist Joe Armon-Jones and the drummer Moses Boyd.

Her first release was the six-track EP Nubya's 5ive, issued on the Jazz Re:freshed label on May 9, 2017, with Armon-Jones on piano, Daniel Casimir on bass, Femi Koleoso and Moses Boyd sharing the drums, and Sheila Maurice-Grey (trumpet) and Theon Cross (tuba) added on selected tracks. That year her band opened at Gilles Peterson's Worldwide Festival in Sète, France, and in 2018 she played the Winter Jazzfest in New York and JazzFest Berlin. Her second EP, When We Are (March 8, 2018, on the Nyasha imprint), explored the use of electronics in a live jazz setting and was made with support from the Steve Reid InNOVAtion Award, a development grant from the PRS Foundation and the Steve Reid Foundation. In the same years she played in the collectives Nérija and Maisha, appeared on records by Sons of Kemet and others from the London scene, and began a monthly radio show on NTS in November 2017. She was named UK Breakthrough Act at the Jazz FM Awards in April 2018, won the Times Breakthrough Award at the 2018 South Bank Sky Arts Awards, and took UK Jazz Act of the Year at the 2019 Jazz FM Awards.

Source, her first studio album, came out on Concord Jazz on August 21, 2020. She produced it with Kwes, with a band that included Armon-Jones, Casimir and the drummer Sam Jones; it was recorded at Soup Studio in London, apart from the cumbia piece "La Cumbia Me Está Llamando," which was recorded at Mambo Negro Studios in Bogotá, Colombia. The record was shortlisted for the 2021 Mercury Prize in July of that year. A Record Store Day EP of remixes, Source ⧺ Our Dance, followed in June 2021, and the full remix album Source ⧺ We Move appeared on October 22, 2021, with reworkings by Georgia Anne Muldrow, KeiyaA, Kaidi Tatham, Moses Boyd and Nala Sinephro, among others. On August 18, 2021, she debuted her band at the BBC Proms in London's Royal Albert Hall, a concert The Daily Telegraph gave five stars. In December 2020 she joined London Brew, a band of British jazz musicians assembled around Miles Davis's Bitches Brew; its self-titled album, with Garcia on saxophone and flute, was released on Concord Jazz on March 31, 2023.

She performed with the band Khruangbin at Radio City Music Hall in New York, and the March 9 and 10, 2022 shows were released in 2023 as the live album Live at Radio City Music Hall, which carries both acts' names. On September 15, 2023, at London's Royal Festival Hall, she performed with the Nu Civilisation Orchestra in a concert built around Stan Getz's 1962 album Focus. Four singles ("Lean In," "Fortify," "Nubya's Side of Town" and "The Seer") led up to her second studio album, Odyssey, released on Concord Jazz on September 20, 2024. She produced it with Kwes, wrote and orchestrated the string parts for players from the Chineke! Orchestra, and used a band of Armon-Jones, Casimir, Sam Jones and the percussionist Jansen Santana, with vocal guests Esperanza Spalding, Georgia Anne Muldrow and Richie Seivwright. It holds a Metacritic score of 83 from nine reviews, and she was nominated for UK Jazz Act of the Year and Album of the Year (for Odyssey) at the 2025 Jazz FM Awards, which went to corto.alto and Ezra Collective respectively.

Concord announced a North American tour for 2025 in support of Odyssey, and in 2026 she was nominated for Best Jazz Act at the MOBO Awards, which went to Ezra Collective. In October 2026 she played a residency of six sold-out shows at Blue Note London with Lyle Barton on piano and keyboards, Max Luthert on bass and Sam Barrell Jones on drums, no set repeating across the week, and tried out new compositions that she said might be recorded in a coming studio session, according to All About Jazz's review of the run. As of November 2026 her most recent album is Odyssey.

Garcia is a tenor saxophonist who writes for a working band, usually with Armon-Jones on piano or electric piano, and builds pieces on modal vamps, dub and reggae bass lines, Latin American rhythms and, on Odyssey, orchestral strings. The twelve-minute title track of Source was described by The Line of Best Fit as a blend of dub and modal jazz, and she has tied its feel to reggae and lovers' rock. Live, All About Jazz heard her in hard-blowing form on "Pace" and in a breathy ballad mode on a new piece, with echoes of Wayne Shorter and Ben Webster in her solos. She names the saxophonists Dexter Gordon, Sonny Rollins and John Coltrane, the trumpeter Miles Davis and the pianist-composer Mary Lou Williams as her musical heroes, and the Birmingham reggae band Steel Pulse among her inspirations. Her heritage runs through the writing: she introduced "Before Us: In Demerara & Caura" on Source as an acknowledgement of her parents' Guyanese and Trinidadian roots. She came up through Tomorrow's Warriors and the Jazz Re:freshed label alongside Armon-Jones, Boyd, Cross and Maurice-Grey, part of a London generation that mixed jazz with dub, Afro-Caribbean music and electronics. Jazzwise gave Odyssey four stars and an Editor's Choice mark.