The squadron moved to RNAS Lewiston, Maine, United States, at the end of July 1943 and also providing advanced carrier training to American-trained Royal Naval Volunteer Reserve (RNVR) pilots and it later provided complete Torpedo Bomber Reconnaissance (TBR) aircrew for Grumman Avenger FAA squadrons.

[4] Quonset Point was a United States Naval Base loaned to the Admiralty from 1 October 1942 and commissioned as HMS Asbury.

It was used by the Royal Navy for forming and working up Fleet Air Arm squadrons, operating with American aircraft supplied under the Lend-Lease agreement, although it later recommissioned as HMS Saker II, on 13 March 1943.

[2] Its role was to take newly qualified FAA pilots and instruct them in the techniques of air-to-air combat and air-to-ground firing.

[2] April 1954, until it moved to RNAS Yeovilton in 1956, saw the Command Instrument Grading and Examination Flight attached to 738 Naval Air Squadron.

[9] During the rest of the decade, the squadron lost (December 1958), and then later regained (June 1960, again from 736 Naval Air Squadron), Hawker Sea Hawk aircraft, but it took the de Havilland Sea Venom FAW.21, a carrier-capable jet fighter-bomber aircraft, used as an all-weather interceptor aircraft by the FAA, for all weather fighter training from October 1957 until September 1960, and later provided the Sea Venom Operational Flying School Parts I and II.

On 6 January 1964, 738 Naval Air Squadron relocated to RNAS Brawdy (HMS Goldcrest) in Pembrokeshire, Wales,[10] where it operated as phase 2 of the Advanced Flying Training course, giving tuition on fighter tactics and weapons release to students graduating out of 759 Naval Air Squadron, which was also based at RNAS Brawdy.

[2] Using three Hawker Hunter GA.11 aircraft and a single Hawker Hunter T.8 two-seat trainer aircraft, a Fleet Air Arm aerobatic team was formed from 738 Naval Air Squadron, led by Lieutenant Commander Chris Comins, RN, whilst at RNAS Brawdy (HMS Goldcrest).