Tanya Darby was born and raised in Seaside, California, on the Monterey Peninsula. She came up through the Monterey Jazz Festival's own youth big band, the Next Generation Jazz Orchestra, playing in it as a student before later returning as a guest judge; the ensemble's longtime conductor, Paul Contos, called her "one of our finest success stories" in a 2018 interview. She earned a bachelor's degree in jazz performance from the Manhattan School of Music in 1998 and, more than a decade into her professional career, a master's degree in jazz performance from Rutgers University in 2012.

Darby built her career inside the New York big-band circuit, holding chairs in the Vanguard Jazz Orchestra, the Roy Hargrove Big Band, the DIVA Jazz Orchestra, the Michel Camilo Big Band, the Rufus Reid Large Ensemble, the Manhattan Jazz Orchestra, Jimmy Heath's Queens Jazz Orchestra and the Frank Foster Loud Minority Big Band, frequently as lead trumpet. She has performed and toured as a guest with the Count Basie Orchestra, the Duke Ellington Orchestra, the Cab Calloway Orchestra, the Ron Carter Great Big Band, the George Gruntz Concert Jazz Band, and Paquito D'Rivera and the United Nations Orchestra. She has repeatedly guested with the Jazz at Lincoln Center Orchestra under Wynton Marsalis, documented on dates including the February 2015 "Jazz Titans: Duke, Dizzy, 'Trane and Brubeck" concerts in Chicago, Ann Arbor and Toronto, and the May 2018 "Swingin' Thru H-Town" concert with the Jazz Houston Orchestra in Houston. Her non-big-band work has included touring and performance credits with Dianne Reeves, Clark Terry, Jon Faddis and Frank Foster; a television appearance on BET on Jazz with the T.S. Monk Sextet; and a spot in Aretha Franklin's horn section for the Arista Records 25th Anniversary Special, broadcast on NBC.

In 2006 Darby was one of three trumpet and flugelhorn chairs, alongside Avishai Cohen (trumpet) and Frank Greene, in the big band that clarinetist and saxophonist Anat Cohen and arranger Oded Lev-Ari assembled for a single studio date at Avatar Studios in New York. The record, Noir, was released on Cohen's own Anzic Records in April 2007 under the billing "Anat Cohen & The Anzic Orchestra"; the ensemble is profiled in full at The Anzic Orchestra. Darby's own big-band credits away from that one-off date have twice reached the Grammy Awards: the Vanguard Jazz Orchestra's OverTime: Music of Bob Brookmeyer and Rufus Reid's Quiet Pride: The Elizabeth Catlett Project, both recorded in 2014, were nominated at the 57th Grammy Awards in 2015, the Reid album picking up nominations in both the Best Large Jazz Ensemble Album and Best Instrumental Composition categories. Earlier in her career, the Bobby Sanabria Big Band's live Birdland recording Afro-Cuban Dream... Live & In Clave!!!, on which she also played, was nominated for Best Latin Jazz Album at the 2001 Grammy Awards. She also appears on Terri Lyne Carrington's 2015 album The Mosaic Project: Love and Soul, playing trumpet on four of its twelve tracks alongside fellow section trumpeter Arnetta Johnson and, on other tracks, Ingrid Jensen.

Alongside performing, Darby built a parallel career in jazz education. She held adjunct faculty positions at Temple University and The New School in New York before moving to Texas to become an assistant professor of jazz trumpet at the University of North Texas. In November 2018 Berklee College of Music announced her as the incoming chair of its Brass Department, effective that January; Berklee's dean of the Professional Performance Division, Ron Savage, said at the time that "Darby's impressive background in performance and education will contribute tremendously to the goals and initiatives of the Brass Department at Berklee." Berklee's own current faculty listing carries her as a professor within the Brass department, teaching brass improvisation, lead trumpet styles, private instruction and recital preparation; she has also served on the guest faculty of Birch Creek Music Performance Center and the Apex Trumpet Symposium, and works widely as a clinician and adjudicator at festivals in the United States and abroad.

Darby's reputation rests on the lead trumpet chair, the seat inside a big band responsible for setting phrasing, dynamics and articulation for the whole brass section, and she has held it across an unusually wide range of ensembles: the Thad Jones/Mel Lewis lineage carried forward by the Vanguard Jazz Orchestra, the swing-era repertoire of the Count Basie and Duke Ellington orchestras, the harder-driving Roy Hargrove and Michel Camilo big bands, and the all-women DIVA Jazz Orchestra. That range, moving convincingly between repertory swing charts and contemporary big-band writing without a signature "sound" of her own imposing itself, is itself the mark of a first-call lead player rather than a stylistic innovator, and it is the same skill set her Berklee teaching load (lead trumpet styles, brass improvisation) is built to pass on.