Clinton Joseph Houston was born in New Orleans on June 24, 1946, spent his early childhood in Washington, D.C., and grew up from adolescence in Queens, New York. He started piano lessons at ten and turned to jazz in his early teens after hearing Cannonball Adderley on the radio. The switch to double bass was not a calling but a consolation prize: turned down for the pianist's chair in his high school band, he took up the instrument nobody else wanted. He played Latin dance music at neighborhood parties in a group called the Jazz Samaritans, taking his cues from Art Blakey records, and at nineteen won a Jazz Interactions competition that put him in front of Paul Chambers, who told him to keep going. His parents steered him toward architecture at the Pratt Institute; he transferred to Queens College to study music and finally took a degree in graphic art from Cooper Union, a training he later used on his own album sleeves.

Through college he spent weekends in the house band at Slug's Saloon on East Third Street, playing the Sunday matinees with pianist George Cables and drummer Lenny White. The three grew up in the same Queens circle as Billy Cobham, Steve Grossman and trumpeter Charles Sullivan, and the bandleaders passing through Slug's began hiring them. Houston was a founding member of the musicians' co-operative Free Life Communications with Dave Liebman, which anchored him in the New York loft scene of the early 1970s. The first documented sessions came quickly: Nina Simone's band in 1969, Roy Haynes in 1969 and 1970, the Toronto dates of January 27 to 29, 1970 that produced Sonny Greenwich's The Old Man and the Child and Don Thompson's Love Song for a Virgo Lady, and then Woody Shaw's debut Blackstone Legacy, cut December 8 and 9, 1970 at A&R Studios with two bassists split across the stereo image, Ron Carter on the left channel and Houston on the right.

From 1971 to 1973 he held the bass chair in Roy Ayers's Ubiquity, documented on Live at the Montreux Jazz Festival (recorded June 20, 1971) and Red Black & Green (1973). It was a well-paid job he came to resent, because Ayers increasingly wanted electric bass and Houston wanted to play upright. In December 1972 he took the opposite tack entirely, recording an album with the co-operative quartet Friends, alongside guitarist John Abercrombie, saxophonist Marc Cohen (later known as Marc Copland) and drummer Jeff Williams, taped through Columbia University's radio station WKCR and issued on the tiny Oblivion label. Houston contributed the tune "Black Vibrations." He then joined Charles Tolliver's Music Inc for the 1973 to 1975 stretch, a band that took him from a club date in Edmonton on June 24, 1973, his twenty-seventh birthday, to Yubinchokin Hall in Tokyo on December 7, 1973 for Live in Tokyo, and finally into Tolliver's expanded orchestra for Impact.

The association that defined him began in Stan Getz's quartet, where he found himself next to pianist Joanne Brackeen and drummer Billy Hart. The band's first surviving studio date is October 1, 1975, later issued as The Master, and its high point is the week of May 11 to 16, 1976 at San Francisco's Keystone Korner with João Gilberto, tapes that stayed in a vault for forty years before Resonance released them in 2016 as Getz/Gilberto '76 and Moments in Time. Getz told the journalist Ted Panken more than once that no band had ever supported him so completely. Houston and Brackeen kept working together until 1986, an eleven-year partnership that produced her Invitation (recorded July 14, 1976 in Weesp, Holland), AFT, Tring-a-Ling, and the duo album they made the very next day in the same Dutch studio, New True Illusion, released on Timeless with both names on the sleeve.

His own leader catalog is small, four records across thirteen years, and all of it came out on European or Japanese labels. Watership Down, cut February 13 and 14, 1978 at C&I Recording in New York, was released only in Japan on Whynot: Houston produced it, arranged it, wrote four of its six tunes, and designed the cover himself, with Brackeen and Onaje Allan Gumbs on keyboards, Abercrombie on guitar and Al Foster on drums. Inside the Plain of the Elliptic followed on the Dutch Timeless label, recorded April 18 and 19, 1979 with Brackeen, Ryo Kawasaki on guitars and Rubens Bassini on congas, and no drummer at all; Houston played acoustic guitar as well as both basses and arranged the entire program. The Japanese connection ran deeper than the labels: he toured Japan with Terumasa Hino in 1977, played the Live Under the Sky festival at Tokyo's Denen Colosseum that July, and was the bassist on John Scofield's first album as a leader, recorded in Tokyo in August 1977 and issued there as John Scofield before the West got it in 1987 retitled East Meets West.

Woody Shaw hired him for the quintet that made the trumpeter's Columbia records between 1977 and 1979: Rosewood (recorded that December, a Grammy nominee and DownBeat's readers' album of 1978), the Village Vanguard live set Stepping Stones from August 5 and 6, 1978, and Woody III. After that Houston worked steadily rather than prominently. He was the bassist on Pepper Adams's last great live document, recorded August 19 and 20, 1983 at Fat Tuesday's in New York with Kenny Wheeler, Hank Jones and Louis Hayes, and issued as Live at Fat Tuesday's and later Conjuration. In 1988 he made a trio record of standards in New York with Roland Hanna and Lewis Nash, The Bar, again for a Japanese label. From 1989 to 1994 he anchored Hayes's quintets and sextets on five SteepleChase and Candid albums, reunited there with Tolliver and playing beside Kenny Barron, and he spent the early 1990s in Hamiet Bluiett's pianoless quartet with Ted Dunbar and Ben Riley. His last documented session was Bob Ackerman's Big Daddy in 1997. Clint Houston passed away in New York City on June 7, 2000, at fifty-three. His wife Gerry Houston, who worked the door at the Village Vanguard and died in 2009, is thanked by name on the sleeve of Watership Down; when Resonance finally issued the 1976 Getz tapes in 2016, the album was dedicated to the memories of Getz and Houston.

Houston solo'd like a horn player, and said so: what he was after on the bass was texture, notes chosen fast enough and close enough together that an arpeggio would land on the ear as a chord. Joanne Brackeen, who played with him for fourteen years, described exactly that, a soloist's temperament in a rhythm-section job with no motive behind it beyond loving to do it. He engineered his instrument to allow it, setting the E and A strings high off the fingerboard for resonance and the D and G low for speed, running Barcus-Berry and Polytone pickups by 1978, and using a hybrid of the German and Italian left-hand positions that he taught to his private students. His main instrument was a Czechoslovak double bass built in 1940 that he found for sale in a recording studio and named Gertrude; he also owned a clear Plexiglas electric bass, which he played under protest during the Roy Ayers years. He was a real composer as well, writing four of the six tunes on Watership Down and four of the six on Inside the Plain of the Elliptic, and placing originals on records by Woody Shaw, Louis Hayes, Carter Jefferson, Gary Bartz and Hamiet Bluiett. AllMusic's biography puts the reputation problem plainly, calling him "underrated by everyone except the musicians who play with him."