Grace Kelly was born Grace Chung on May 15, 1992, in Wellesley, Massachusetts, to Korean parents, and moved to Brookline when she was two. She tried clarinet and classical piano before settling on the saxophone, which she has said reminded her of a human voice. Her mother married Robert Kelly in 1997, and he legally adopted her a few years later, which is how she came to share her name with the film actress who became Princess of Monaco; Kelly has said she signed her first-grade papers "Princess Grace Kelly" after seeing High Society. She wrote her first song, "On My Way Home," at seven, and on March 15, 2005, at twelve, she released her first CD, Dreaming, on PAZZ Productions, the imprint that has issued nearly all her records. The cabaret singer Ann Hampton Callaway, whom she met while the record was being made, wrote its liner notes. Times Too followed in 2005 and Every Road I Walked in 2006; the title piece of the latter won her first ASCAP Foundation award at fourteen and was the basis of her first full orchestral arrangement, written for a performance with the Boston Pops.

In 2006, at a summer jazz residency program at Stanford where he was teaching, she met the alto saxophonist Phil Woods, and a few months later at one of his gigs in Pittsfield, Massachusetts, he invited her on stage and gave her his trademark leather cap after her solo on "I'll Remember April." She left Brookline High School at sixteen and earned a GED, studied in the jazz department of the New England Conservatory's preparatory school, and then enrolled at Berklee College of Music, where she graduated in December 2011 with a degree in professional music at nineteen. Her saxophone teachers included George Garzone, Lee Konitz, Allan Chase, Greg Osby, Jerry Bergonzi, Jeremy Udden, and James Merenda.

Her breakthrough records came while she was still a teenager. GRACEfulLEE (2008) paired her with Konitz, bassist Rufus Reid, guitarist Russell Malone, and drummer Matt Wilson, earned four and a half stars from DownBeat, and was later named among that magazine's best albums of the 2000s. Mood Changes, a quintet date with trumpeter Jason Palmer, pianist Doug Johnson, and drummers Jordan Perlson and Terri Lyne Carrington, was released on May 5, 2009, and two of its pieces won 2008 ASCAP Young Jazz Composers and DownBeat student awards. In 2009 she played the Kennedy Center with Dave Brubeck and the Foxboro High School jazz ensemble and, at Wynton Marsalis's request, sat in with the Jazz at Lincoln Center Orchestra during the events around Barack Obama's inauguration; that summer a New York Times reviewer caught her at Dizzy's Club Coca-Cola and praised her crisp alto tone. In 2010 she joined Dee Dee Bridgewater, Geri Allen, Carrington, and Esperanza Spalding in an all-star quintet at the Kennedy Center's Mary Lou Williams Women in Jazz Festival. She recorded Man with the Hat with Woods on June 12, 2010, at Red Rock Recording in Saylorsburg, Pennsylvania, with pianist Monty Alexander; it came out on January 25, 2011, and she followed it that year with Grace, an album of hymns and gospel songs.

From 2012 she played the 30th annual NEA Jazz Masters ceremony with Woods, Marsalis, and the Jazz at Lincoln Center Orchestra, toured Madagascar and the Comoros on a U.S. State Department speaker program, and began teaching residency workshops at Berklee. Live at Scullers (February 2013) documented her touring band at the Boston club, and her 2013 single "Sweet Sweet Baby," released by Woodward Avenue Records, reached the Billboard Smooth Jazz Singles chart. The five-song EP Working for the Dreamers (September 2014) was produced by Stewart Levine. That year she was also a featured performer in the Frank Morgan documentary Sound of Redemption, and she played a tribute concert at the Grammy Museum on June 15, 2014 with George Cables, Ron Carter, Mark Gross, and Roy McCurdy. Vanity Fair profiled her as a significant millennial in jazz in December 2015, and DownBeat's 2016 Critics Poll named her its Rising Star on alto saxophone. Trying to Figure It Out (2016), which pairs acoustic jazz and cinematic pieces with contemporary production and features Jon Batiste, Michael League of Snarky Puppy, and the remixer Mocean Worker, includes "Blues for Harry Bosch," written for the Amazon series Bosch, in which she appears as herself in a 2016 episode; The Manhattan Transfer later recorded the piece on The Junction (2018).

She has performed many times with Batiste and his band Stay Human on the Late Show with Stephen Colbert, and in September 2017 she organized an all-star benefit at the Berklee Performance Center that endowed the Fred Taylor Scholarship Fund. Her own band records, Go Time: Brooklyn and Go Time: Brooklyn 2 (both 2018) and Go Time: Live in LA (2019), set jazz standards and covers beside funk, pop, and electronic production, and "Feels Like Home" won Song of the Year at the 2018 John Lennon Songwriting Contest. The baritone saxophonist Leo Pellegrino guested on Go Time: Brooklyn 2, and on November 30, 2019 the two announced the alto and baritone duo 2SAXY; she also co-founded the online Saxy School with him. All That I Need (2022) draws on the writing of Maya Angelou and supports the nonprofit She's the First, and in 2022 she became the youngest member of Berklee's board of trustees, where the college's website lists her as a trustee. On March 1, 2024 she released At the Movies, a string-orchestra record of film themes modeled on Charlie Parker with Strings, produced by Bryan Carter with arrangers including Charlie Rosen and Steven Feifke and guests Sean Jones and Cory Wong, which she described as her first jazz record since 2016.

Kelly is a bebop-rooted alto saxophonist and a singer-songwriter with a pop streak, and her catalog divides accordingly: the Konitz and Woods records, Mood Changes, and At the Movies are straight-ahead and orchestral jazz, while Trying to Figure It Out, the Go Time sets, and All That I Need blend jazz with funk, pop, and electronic production. Her first alto hero was Charlie Parker, whose Charlie Parker with Strings shaped At the Movies, and as a teenager she recorded with two elder altoists, Lee Konitz and Phil Woods, extending Woods's bebop lineage on Man with the Hat. Reviewers of her early records praised a crisp tone and a style free of stock patterns, and JazzTimes called her singing supple and pure beyond her years. Her Yamaha biography describes her approach as an avoidance of restrictive labels, and her career spans both jazz honors (Berklee's biography counts her as a nine-time winner of the DownBeat Critics Poll in the Rising Star Alto Saxophone category) and mainstream work such as national advertising campaigns and television appearances.