The T73's lineage ran through the Cooper T70, a car Bruce McLaren had persuaded Cooper to build for the 1964 Tasman Series, itself derived from the 1963 T66. The T73 retained a tubular steel chassis, reinforced with additional stressed steel panels welded to the floor and sides. Front suspension used double wishbones with inboard spring-damper units connected by rocker arms; the rear featured a lower wishbone, trailing arm, and upper link. Because the Tasman T70 had been designed for shorter races requiring less fuel, the T73 was fitted with additional pannier fuel tanks to meet the demands of European Grand Prix distances. Power came from the Coventry Climax FWMV V8, transmitted through a Cooper six-speed gearbox.
The T73 debuted at the 1964 Monaco Grand Prix with Bruce McLaren and Phil Hill as the works drivers. McLaren broke a wishbone during practice and was forced to use the previous year's T66 for the race; Hill retired with suspension failure. The rest of the season produced isolated bright spots amid general disappointment. McLaren achieved second-place finishes in Belgium and Italy, ending the year seventh in the Drivers' Championship. Hill had a far harder campaign, scoring just a single point. In Austria, Hill crashed both his T73 and the team's spare T66, leading to a temporary dismissal by John Cooper and his absence from the Italian Grand Prix, where he was replaced by John Love. Cooper finished fifth in the Constructors' Championship.
McLaren and his new teammate Jochen Rindt took the T73 to the 1965 South African Grand Prix, after which it was superseded by the newer T77. Rindt briefly reverted to a spare T73 at the Italian Grand Prix when valve damage sidelined his regular car.
One of the works T73s was subsequently acquired by J.A. Pearce Engineering, who fitted it with a Ferrari GTO 3-litre V12 and campaigned it in British club events during 1966 and 1967 with Chris Lawrence driving. The car was not especially successful in this configuration, though it did record a fifth-place finish in the 1966 International Gold Cup.
A hybrid variant known as the T71/73 was built by Bob Gerard Racing, blending the T73 body with a Formula Two T71 chassis and powered by a 1.5-litre Ford Twin-Cam engine. This car was entered in the British Grand Prix in both 1964 and 1965.
The T73 was a competent but ultimately mid-field car during an era in which Lotus, BRM, and Ferrari had developed more sophisticated technology. Its modest results in 1964 foreshadowed the larger difficulties Cooper would face as the decade progressed and the team navigated the change to the 3-litre formula without the resources or the personnel needed to mount a genuine championship challenge.