Andy Hunter was born on July 30, 1979 in Grayling, in the north of Michigan's Lower Peninsula, and went through the Interlochen Arts Academy before Oberlin. He took two degrees there at once: a Bachelor of Music from the Oberlin Conservatory, where he studied trombone with Robin Eubanks, and a Bachelor of Arts in Chinese language and literature from Oberlin College. His earliest appearance on record is the Oberlin Jazz Ensemble's Spring, '98, a split CD with the Oberlin Jazz Septet on which he plays the six large ensemble tracks under Wendell Logan's direction. He had already won a DownBeat Student Music Award for jazz composition in 1996.

The decade after Oberlin was split between three cities. In Cleveland he taught on the jazz faculty of Tri-C College, played horn sections at the Rock and Roll Hall of Fame behind Motown acts, and worked in Latin bands: he wrote or arranged three of the tracks on Sammy DeLeon y su Orquesta's Con Salsa y Sabor! (Azica, 2003) and played on Ernie Krivda and the Fat Tuesday Big Band's Body & Soul, recorded in September of the same year. His Chinese degree took him to Shanghai, where he recorded The Slow Road to Shanghai with his own quartet in August 2004 and later made dates with the guitarist Lawrence Ku and the bandleader Alvaro Cardenas. He moved to Brooklyn in 2004, took a master's in jazz at Rutgers University studying with Conrad Herwig, and then taught on the Rutgers jazz faculty himself. The competition results came in that stretch: he won the International Trombone Association's Frank Rosolino Jazz Trombone Competition in 2002, was a finalist in the 2003 Thelonious Monk International Jazz Competition, and won the Antti Rissanen International Trombone Competition in Finland in 2005 and the ETW National Jazz Trombone Competition in Washington, D.C. in 2006.

New York put him in the trombone sections of most of the city's standing large ensembles. He was a regular member of the Mingus Big Band and its sister groups Mingus Dynasty and the Mingus Orchestra, of the Toshiko Akiyoshi and Lew Tabackin Jazz Orchestra, which recorded him in Shanghai in October 2010 for In Shanghai, and of Tommy Igoe's Birdland Big Band, whose Eleven was cut at Avatar Studios in 2011. He played Orrin Evans' Captain Black Big Band on Mother's Touch (Posi-Tone PR8123), took the trombone chair in the Fat Cat Big Band from Jonathan Voltzok by 2010, and toured with the Dave Holland Big Band, the Richard Bona Group, T.S. Monk's "Monk on Monk" ten-piece, Nnenna Freelon and Travis Sullivan's Bjorkestra. The Latin work ran in parallel, with the Cuban charanga La Típica Novel, the Grammy-nominated Ochún, La Cumbiamba eNeYé and Hector Martignon's Banda Grande, and behind salsa singers including Rubén Blades and Gilberto Santa Rosa. His own band of the period was SPOKE, a co-operative quartet with the bassist Dan Loomis, the saxophonist Justin Wood and the drummer Danny Fischer that recorded three albums from April 2008 onward, roughly half of each written and arranged by Hunter. He also played Snarky Puppy's groundUP, taped live and without overdubs at Shapeshifter Lab in Brooklyn on December 14, 15 and 16, 2011; David Binney's Third Occasion (Mythology, 2009); the seven Brass Carnival pieces on Earl McIntyre's Brass Carnival & Tribute!, recorded at Bennett Studios on October 2, 2010 with David Amram conducting; and Riccardo Fassi's New York Pocket Orchestra date Sitting in a Song, alongside Antonio Sanchez, Gary Smulyan and Alex Sipiagin.

Think Like a Mountain, recorded in Brooklyn in April 2010 and issued on his own River Records imprint (RRCD 001) on October 1, 2012, was his first album as a leader to circulate internationally. It is a sextet of Mingus Big Band alumni: Alex Sipiagin on trumpet, Jason Marshall on baritone saxophone, David Kikoski on keyboards, Boris Kozlov on bass and Danny Fischer on drums, playing six Hunter originals against two standards. Reviewing it for DownBeat in 2013, Ken Micallef wrote that Hunter, Sipiagin and Marshall play like separate fingers from the same hand, and the International Trombone Association Journal called it music making at the highest level.

The connection that runs longest through his sideman work is with the Israeli saxophonist Shauli Einav, whose first three albums all have Hunter's trombone as the second horn. Opus One (Plus Loin Music PL4534) was recorded at Peter Karl Studios in Brooklyn on March 23, 2010 and released on January 11, 2011, a New York quintet with Shai Maestro on piano, Joseph Lepore on bass and Johnathan Blake on drums; the album's own credit block on Einav's Bandcamp names those five players and no guests. A Truth About Me (Cristal Records CR218, October 25, 2013) moved the band to Paris, with Paul Lay on piano, Florent Nisse on bass and Louis Moutin on drums; Hunter plays all ten tracks, while Antonin-Tri Hoang's alto saxophone and bass clarinet are restricted to four of them. Animi (Berthold Records and Outside In Music, OIM1936), recorded at the Studio de Meudon on March 25 and 26 and August 28, 2018, added Tim Collins on vibraphone, Yoni Zelnik on bass, Guilhem Flouzat on drums and Fayçal Salhi's oud on a single track. Hunter is the only member of that band besides Einav who wrote for it: the seventh piece, "Si Lu," is his.

Since the autumn of 2012 he has held a permanent chair in the WDR Big Band Köln, playing third trombone, and his discography since then has largely been that orchestra's guest-artist series. He is on Ron Carter's My Personal Songbook, cut in WDR's Studio 4 in July 2014; on both of Marshall Gilkes' WDR records, Köln (recorded January 2014) and Always Forward (September 2017); on Vince Mendoza's Homecoming, taped live at the Philharmonie in Cologne on November 21, 2014, where he takes the solo on "Choros #3"; and on Fred Hersch's Begin Again (Palmetto, 2019), where he is billed as third trombone and solos on "Forward Motion." The same chair put him on records with the Yellowjackets, with Eddie Gomez and Steve Gadd, with Steps Ahead and Mike Mainieri, with Luciana Souza, Dave Stryker and Andrea Motis, on Bill Dobbins' big band setting of Bach's Goldberg Variations, and on Kurt Elling's In the Brass Palace, where he is the featured trombone on "They Speak No Evil." Outside the orchestra he co-led Confluence (River Records, November 3, 2017) with the Swedish alto saxophonist Johan Hörlén, a quintet with Tim Collins on vibraphone, John Goldsby on bass and Adam Nussbaum on drums that sets Hunter and Hörlén originals against Joe Henderson's "Inner Urge" and Mal Waldron's "Warm Canto." He writes about half the book for the Latin jazz quintet Viento Terral, whose Eh'Neeky! appeared in 2016 and whose Tunnel Visionaries (2023) features Bob Mintzer, plays in the salsa band Marcando, and is a featured soloist with the Mambísimo Big Band. He has taught at the Codarts conservatory in Rotterdam alongside Ilja Reijngoud since 2015, and plays a Rath R3F custom trombone.

Hunter's teachers were two of the most technically formidable trombonists of the generation ahead of him, Robin Eubanks at Oberlin and Conrad Herwig at Rutgers, and the writing on his own dates points to a third source that neither of them accounts for: the ensemble sound of the Mingus Big Band, where he spent years and from which he recruited every member of the Think Like a Mountain sextet. Reviewers of that album kept describing the same quality, a horn section voiced so tightly that three players read as one instrument, and an earlier All About Jazz notice on SPOKE had already singled out the range of colors he pulls from the horn, from something close to a trumpet's clarity to the blatt of a tuba. He is unusual among American big band trombonists in how much of his working life has been spent inside other traditions: Cuban charanga and Colombian cumbia in New York, salsa in Cleveland and again in Cologne, and a Chinese degree that produced both a Shanghai quartet album in 2004 and, fifteen years later, the tune "Si Lu" on Shauli Einav's Animi. The competition record, four wins and a Thelonious Monk finalist placing between 1996 and 2006, is one measure of the playing; the more telling one is that a German radio orchestra hired an American in his early thirties for a permanent chair and has kept him in it ever since.