The existing T.1 design was developed and Hunting Percival made several improvements to the airframe. Internally the Armstrong-Siddeley Viper 5 engine had been replaced with the more powerful Viper 8 (Viper 102), capable of 1750lbs ofthrust which was employed in the T.2 version. The Canopy had been re-designed allowing the instructor and pupil better all-round vision from the cockpit, and the design was fitted with two Martin-Baker ejection seats for the first time. The wings were also strengthened allowing two tip fuel tanks to be carried on either wing, and three shortened undercarriage units tested on the T.2 replaced the "long-legged" units employed on the production T.1.

The first aircraft off the production line (XM346) took its maiden flight on 22nd June 1958.
Just six days later it was handed over to the Royal Air Force, with the next example following a month later. As with most new aircraft types coming on strength with the RAF, the first aircraft delivered were initially sent to the Aircraft Armament and Experimental Establishment (AA&EE) based at Boscombe Down. This occurred so that the aircraft could be tested thoroughly by the resident team of test pilots, to ensure there were no major problems in the type before entering widespread RAF service.

Three further examples were delivered in the latter part of 1958, with 37 following in 1959.
The T.3s initially went into service with 2FTS, the same unit that adopted the T.1, but at the Squadron's new base at RAF Syerston. In the summer of 1960 the first "all-jet" training course was completed, a major milestone.

As more and more aircraft came onto strength in 1959-60, Squadrons were beginning to re-equip with Jet Provosts, and others were created. The Central Flying School (CFS) based at RAF Little Rissington and the Royal Air Force College (RAFC) based at RAF Cranwell were the two first units to trade in their Piston Provosts for the Jet variety in 1959.
Also adopting the type as more aircraft came on strength, were three other Flying Training Schools (FTS); 1FTS based at RAF Linton-on-Ouse, 6FTS based originally at RAF Acklington, then later at RAF Finningley, and 7FTS based at RAF Church Fenton.
In 1961 RAF Leeming, at a time when many fighter command airfields were closing, received a reprieve when it was transferred to training command. 3FTS was moved onto the airfield and the 'JP' 3 was introduced in October that year.
A late 'new' user of the type was the Tactical Weapons Unit (TWU) at RAF Chivenor, who used the type for training alongside their existing Hunter and Hawk aircraft.

Of 201 T.3 Jet Provosts ordered, all were built and delivered to the RAF between 1958 and 1962. When the last T.3's were coming off the production line Hunting-Percival began development work for a new improved variant, hoping that the RAF would make a further order.

The Jet Provost T.3A remained in use with the RAF's pilot training syllabus for the following 30 years. Some 70 examples were subject to various avionics upgrades by the British Aircraft Corporation (BAC) in the 1970's, and were officially re-classified T.3A's.

Two long-term users of the type were firstly 1FTS based at RAF Linton-on-Ouse, and 3FTS, initially based RAF Leeming but later had periods based at RAF Scampton and Cranwell where it absorbed the Royal Air Force College's aircraft.
Both of these units were the last to trade their final Jet Provost T.3A's examples for the Shorts Tucano in 1992.

The Jet Provost T.3 was exported to three countries, and classified as the Jet Provost T.51. Ceylon ordered 12 aircraft, Sudan received 4 examples and lastly Kuwait bought six aircraft.