Garcia is the daughter of Caribbean immigrants, and along with her siblings, received a grounded and exhaustive musical education. She initially studied violin and moved over to viola to play in the London Schools Symphony Orchestra. She undertook her study of the saxophone at age 10. A natural on the instrument, she joined the Camden Jazz Band and later joined the junior jazz program at the Royal Academy of Music. She also attended the workshops of Tomorrow's Warriors under the direction of Gary Crosby. As a student, she received a scholarship to attend the summer program of the Berklee College of Music in Boston. Back in London, she studied at Trinity Laban Conservatoire of Music and Dance, where she received her bachelor's degree and was celebrated as "a jazz instrumentalist with distinction."
After spending some time working on the London club scene, where she encountered like-minded musicians from Hutchings, Boyd, and Cross to Ezra Collective, Emanative, and Kamaal Williams, she joined drummer Jake Long's Maisha sextet for the 2016 EP Welcome to a New Welcome. The following year she joined the all-female jazz-funk septet Nérija for their self-titled EP. Also in 2017 she issued the self-released Nubya's 5ive mini-album that sold out in a single day and needed to be repressed. Hutchings included her on We Out Here, a compilation album of the new British jazz issued by Gilles Peterson's Brownswood label in 2018, the same year Maisha issued their debut full-length, There Is a Place. Later that annum she dropped her own follow-up leader date, When We Are, that included two new tracks plus remixes by K15 and Maxwell Owin, and toured on her own and with McCraven's transcontinental big band.
In 2019, Garcia won the Jazz FM Breakthrough Act of the Year Award as well as the Sky Arts Breakthrough Act of the Year Award, and took home the Jazz FM U.K. Jazz Act of the Year Award. In 2020, North America's Concord Records signed her to its prestigious jazz roster and issued the digital single "Pace" in celebration of the late May announcement. Produced by Garcia in collaboration with Kwes (Bobby Womack, Solange, Nerija), Source, her debut long-player, was issued in August; it offered a multivalent approach to modern jazz through its engagement with soul, Afrobeat, and dubstep. The album's club influences were expanded upon with 2021's Source: We Move, a remix collection featuring artists like Kaidi Tatham, Nala Sinephro, and Georgia Anne Muldrow. ~ Thom Jurek, Rovi