My own TR3A runs a Stag gearbox with TR6 'A' type overdrive, so no problems with the fitment.
The TR4A transmission is one synchro mesh ring longer than a TR3A gearbox. (4 synchro as opposed to 3 synchro)
This means that the gearbox mounting is about 3/8" too far forward on your TR3A chassis when you put in the TR4A 'box.
Do not push the engine forward, relieve the holes in the chassis cross plate.
**File the two big holes in the chassis mount plate rearwards to accommodate this and use big diameter washers on the studs from underneath.**
The 3 studs at the top of the engine are too short for the TR4A gearbox as the bellhousing flange is thicker on the later 'box.
**Change for longer studs.**
TR3A gearbox has a dip stick filler in the top cover. The TR4A gearbox has not and is filled by a left hand side oil filler hole. I have always found this side filler to be a pain to get at on the TR3A. Be sure the plug is easy to remove.
**Be sure that the side filler hole screwed plug is able to be removed before the gearbox is fitted.**
**Best mod is drill the TR4A top cover to accept the TR3A dipstick. (the moulding mark is on the TR4A top cover). - but not essential.**
Cheers
Peter W