Gregory John Tardy was born in New Orleans on February 3, 1966, into a household of singers: both his parents were trained opera singers, and his mother, Jo Anne Tardy, later worked as a gospel-influenced jazz vocalist. He began on classical clarinet and was good enough at it to aim for an orchestral career, studying with the clarinetists Russell Dagon and Jack Snavely and training at Carroll College and the University of Wisconsin. Saxophone came second and almost by accident: he was asked to cover missing chairs in school ensembles, and then began taking paid work on tenor with funk bands around Milwaukee to help fund his studies.

The decision to leave classical music behind came from a single record. At his older brother's prodding, Tardy listened to the duo recording of John Coltrane and Thelonious Monk playing "Monk's Mood," and committed to jazz on the spot. He studied jazz harmony at the Wisconsin Conservatory of Music, spent about a year on the jazz and blues scene in St. Louis, and then moved back to New Orleans and enrolled at the University of New Orleans, where Ellis Marsalis became his teacher and mentor. The city's rising generation was in the same rooms at the time, and Tardy has named Nicholas Payton, Brian Blade, Victor Goines, Mark Turner and Delfeayo and Jason Marsalis among the players he came up alongside. He also worked the local brass bands and picked up gigs with The Neville Brothers and Allen Toussaint.

Two things happened in 1992. Tardy cut his first record under his own name, Crazy Love, a New Orleans session with Eric Revis on bass, Brian Blade on drums, Peter Martin on piano, Nicholas Payton and Milton Batiste on trumpets and his mother singing. And he was hired into Elvin Jones's Jazz Machine, a job that lasted several years and pulled him to New York. That tenure was a working, touring one rather than a recorded one: no Elvin Jones release carries a Tardy credit in the Discogs catalog. The same is true of his association with Roy Hargrove, which his own biography and his university's faculty page both cite and which left no commercially issued recording behind.

In New York he became a first-call reed player across a strikingly wide range of bandleaders: Wynton Marsalis, Jay McShann, Steve Coleman, Betty Carter, James Moody, Bill Frisell, Rashied Ali and John Patitucci among them. His reputation was made in the second half of the 1990s through three bands in particular. He played clarinet and tenor on Tom Harrell's The Art of Rhythm (RCA Victor, 1998); he joined Dave Douglas's sextet for Soul on Soul (2000) and El Trilogy (2001); and from 1999 he worked in a succession of Andrew Hill's groups, a relationship that ran for years and produced Dusk (Palmetto, 2000), A Beautiful Day (2002) and Time Lines (Blue Note, 2006). Tardy's first major-label date as a leader, Serendipity, came out on Impulse! in March 1998 with Mulgrew Miller and Aaron Goldberg splitting the piano chair, Reginald Veal on bass and Eric Harland on drums; it earned him a Best Debut Artist nomination at the New York Jazz Awards and a European tour on the Rising Stars bill.

When the Verve and GRP merger left him without a home, Tardy moved to smaller labels: J Curve for The Hidden Light (April 2000) and Palmetto for the freer Abundance (2001), which added Miguel Zenón's alto to one track. From 2005 he settled into a long run for the Danish label SteepleChase that produced nine albums in eleven years, from The Truth (2005) through Chasing After the Wind (2016). In 2006 he played tenor saxophone and clarinet on the Brian Lynch/Eddie Palmieri Project's Simpático, which won the Grammy Award for Best Latin Jazz Album; the record's reed section also included Phil Woods, Donald Harrison and Yosvany Terry.

Tardy's later work has moved between two poles. One is his partnership with Bill Frisell, which began with the guitarist's History, Mystery (Nonesuch, 2008), continued as a duo on More Than Enough (Newvelle, 2019) and produced Frisell's quartet record Four (Blue Note, 2022) alongside Gerald Clayton and Johnathan Blake. The other is his own catalog, which since 2020 has appeared on WJ3 Records, the label run by drummer Willie Jones III: If Time Could Stand Still (2020), Sufficient Grace (2022), In His Timing (2023) and Abide in Love (2025), the last recorded at Van Gelder Studios. Tardy is Professor of Jazz Saxophone at the Natalie L. Haslam College of Music at the University of Tennessee, Knoxville, and continues to tour internationally.

Tardy is a tenor player in the modern mainstream line that runs from John Coltrane through Sonny Rollins and Joe Henderson, and he has named Bobby Watson as a particularly important influence; AllMusic describes him as a hard bop player of unusual technique and flexibility with a sound of his own. What separates him from most of his contemporaries is that he never actually abandoned the clarinet, and the doubling is not decorative. On The Art of Rhythm he plays clarinet on four tracks and tenor on four others; on Dave Douglas's Soul on Soul he covers tenor, clarinet and bass clarinet across three separate assignments; and on Frisell's Four he moves between clarinet, tenor and bass clarinet on twelve of thirteen pieces, which is why bandleaders as different as Andrew Hill, Chris Potter, Stefon Harris and Steve Swallow have hired him specifically for the low reeds. He has said he tries to keep the tradition "in the back of my head" without letting it stop him going for what he hears, and the balance shows in the shape of his own records: the SteepleChase and WJ3 albums are mostly his own writing, played by working quintets, with an occasional standard set among the originals. His Christian faith is the other organising thread, stated openly in album titles from Steps of Faith and He Knows My Name through Sufficient Grace and Abide in Love, and it places him in the lineage of jazz musicians for whom devotional material is the subject rather than the packaging.