Harold Floyd Brooks was born on June 7, 1932, in Fayetteville, North Carolina. His nickname, pronounced "Teena," grew out of a childhood pet name, "Teeny." His brother David "Bubba" Brooks was also a saxophonist. The family moved to New York in 1944 and settled in the Bronx, where Brooks started on C-melody saxophone and studied harmony and theory with Herbert Bourne. His first professional work came in 1951 with the rhythm and blues pianist Sonny Thompson, and in 1955 he played with Lionel Hampton. AllMusic also credits him with session work for the R&B singer Amos Milburn. The trumpeter and composer "Little" Benny Harris gave him informal guidance and recommended him to Blue Note producer Alfred Lion.

Brooks's Blue Note years began with sideman dates. On February 25, 1958, he recorded with the organist Jimmy Smith, and Discogs credits him on two tracks of The Sermon! from that session and one track of House Party. On March 16, 1958, at the Van Gelder studio in Hackensack, New Jersey, he made his first session as a leader, Minor Move, with Lee Morgan, Sonny Clark, Doug Watkins, and Art Blakey. It went unissued until Blue Note Japan released it in 1980. In between he played a live Jimmy Smith date at Small's Paradise on April 7, 1958 (issued in 1980 as Cool Blues) and, on May 14, 1958, the sessions that became Kenny Burrell's Blue Lights, where he shared the tenor chair with Junior Cook.

His best-known sideman credit outside the studio was the stage. Jack Gelber's play The Connection, staged by the Living Theater, used a score by the pianist Freddie Redd, with the musicians appearing as characters. Brooks was Jackie McLean's understudy in the production, and on June 13, 1960, he recorded a version of the music with the trumpeter Howard McGhee for the Felsted label. AllMusic calls his work on Redd's score perhaps the most seminal moment of his career as an improviser.

1960 was his busiest year. He played on the debut album of Freddie Hubbard, Open Sesame (June 19), recorded his own True Blue with Hubbard on June 25, and made Shades of Redd with Redd and McLean on August 13. On September 1 and October 20 he led sessions with Blue Mitchell, Kenny Drew, Paul Chambers, and the drummer Art Taylor, the first of them with McLean added. A final leader date, The Waiting Game, followed on March 2, 1961, with the trumpeter Johnny Coles, Drew, the bassist Wilbur Ware, and Philly Joe Jones. Only True Blue appeared in his lifetime, issued in 1960 without much promotion alongside Hubbard's debut. He made no more recordings after 1961.

Heroin dependency and failing health ended his career. Brooks passed away on August 13, 1974, in New York City, of liver failure, at the age of 42. His recorded legacy was assembled after his death. Blue Note Japan issued Minor Move and Street Singer (credited jointly to Brooks and McLean) in 1980, and in 1985 Mosaic Records released a four-LP set produced by Michael Cuscuna, The Complete Blue Note Recordings of the Tina Brooks Quintets, limited to 7,500 numbered sets, which brought out Back to the Tracks and The Waiting Game for the first time. Blue Note put out Back to the Tracks on CD in 1998 and The Waiting Game in Japan in 1999.

Brooks was a tenor saxophonist of the hard bop school with a strong, smooth tone and a steady flow of new melodic ideas. AllMusic's Thom Jurek credits him with stretching the blues framework further than most players of his day, and with a fondness for minor keys and open-ended harmonic figures that his peers envied. He was also a composer: "Street Singer," "Open Sesame," and "Gypsy Blue" are his, and the critic David Rosenthal calls "Street Singer" an authentic hard-bop classic in which pathos, irony, and rage meet in an anguished, sinister performance. Michael Cuscuna, who prepared most of his unissued sessions for release, described him as a sensitive and unique improviser whose lyricism and inner logic were astounding, and argued that lesser talents have been celebrated far more. AllMusic's list of related artists for Brooks includes John Coltrane, Hank Mobley, Dexter Gordon, Charlie Rouse, Booker Ervin, and Sonny Red.