The TR4A was an evolution of the Giovanni Michelotti styled TR4. The car had been favourably received for its overall performance and many amenities but criticized for its harsh ride. The TR4's Hotchkiss drive system was replaced with an independent rear suspension, indicated by an "IRS" badge attached to the TR4A's rear.
Although consideration was given to both an enlarged 2.5 litre four-cylinder or a six-cylinder engine, the TR4A used the same long-stroke, high-torque Standard four-cylinder engine seen in the TR4. While the bore, stroke, and displacement remained the same, changes to the cylinder head and manifolds raised net power to 104 bhp and torque to 132 lb ft.
Apart from the increase in width and the IRS badge on the rear of the car, other changes included a revised grille and new bonnet badge. There was also a new line of chrome trim on the side, starting near the rear edge of the door and ending at the front of the car with integrated signal/marker lights, which were moved from their earlier position in the corners of the grille. New smaller front bumpers and a convertible top patterned after the one from the Herald completed the exterior differences. On the interior the fly-off handbrake lever was moved to the transmission tunnel between two revised seats, the gearshift lever was shortened and the white painted steel dashboard was now always covered by walnut, which had been optional in the TR4.
In response to requests from United States distributors, Triumph developed a version of the TR4A fitted with a TR4-style rear live axle and made IRS an extra-cost option for that market. To locate the newly re-introduced leaf springs, spring brackets were added to the revised chassis. Live axle cars received a commissioning number that started with "CT". This was the same prefix used for TR4s. IRS equipped cars' commissioning numbers began with "CTC".