John Surtees established his eponymous team after leaving BRM, acquiring a McLaren M7C to race while the TS7 was being prepared. Surtees was already a figure of unique standing in motorsport — the only man to have won World Championships on both two and four wheels — and his move into car construction represented an ambitious step for a driver-turned-constructor in the early 1970s. The TS7 was a conventional car for its era, designed in-house with input from Ahmed and Connew alongside Surtees himself.
The TS7 made its competitive debut at the 1970 British Grand Prix, with Surtees driving. He qualified nineteenth and retired with oil pressure failure. In Germany, Surtees qualified fifteenth and was classified ninth despite his race ending in engine failure. A retirement through a blown engine followed at the Austrian Grand Prix, and an electrical failure stalled the car at the start in Italy. The season's best result came at the Canadian Grand Prix, where Surtees qualified and finished fifth, scoring two championship points.
At the United States Grand Prix, Derek Bell joined Surtees as a second driver. Surtees qualified eighth but retired when his engine failed; Bell qualified thirteenth and finished sixth, adding a further point. In Mexico, Surtees ran alone, qualified fifteenth, and finished eighth. The team closed their debut season with three World Championship points, placing eighth in the Constructors' Championship.
As the TS9 — the TS7's successor — became the team's primary car for 1971, the TS7 continued to appear in a supporting role. At the South African Grand Prix, Team Surtees entered three cars: Surtees himself drove the TS9, while Brian Redman and Rolf Stommelen were given TS7s. Stommelen qualified fifteenth and finished twelfth; Redman qualified seventeenth and finished seventh. The race completed the team's use of the TS7 as a works entry, with the squad thereafter concentrating on the TS9.
The Surtees team accumulated eight World Championship points across 1971, placing eighth in the Constructors' Championship for a second consecutive year — all of those points were earned with the newer TS9.
Following its retirement from the Surtees works programme, one TS7 was sold to Dutch organisation Stichting Autoraces Nederland, which entered the car at the 1971 Dutch Grand Prix with local driver Gijs van Lennep. Van Lennep qualified twenty-first and finished eighth in the race.
The Surtees TS7 occupied an important transitional role in the team's development, demonstrating that the constructor could design and race its own competitive machinery in Formula One from a standing start. The car's results were modest — a fifth place and a sixth representing its best finishes — but the TS7 provided the technical learning that fed directly into the TS9 and subsequent designs. The team would go on to be a regular mid-field presence in Formula One through the first half of the 1970s, and the TS7 stands as the starting point of that journey.