Hi Phil,
First, the gearbox needs to be rebuilt around a shorter mainshaft. Then an adapter plate is installed on the rear of the gearbox in place of the extension, to which the OD unit attaches. With A-type or J-type ODs for TRs, the drive shaft is the same. In a TR4, a TR A-type will fit the rear motor mount To use a TR J-type in a TR4 will require some modification of the mount.
(NOTE: there are non-TR A-type and J-type ODs, used in Triumph saloons, Volvos and some other cars, which will not be as easily mounted, but can be adapted.)
If you are re-using the top gearbox cover, it will need to be drilled and tapped for two inhibitor switches to be installed. You'll need a different speedometer cable, a wiring harness, an OD switch on the column (or elsewhere, on my TR4 it's inset in the shift knob), a relay, and a solenoid to operate the OD.
An angle drive on the speedometer cable is optional (was used with a shorter cable on later cars, but not the TR4). There are some interesting modern options, too. For example, Revington TR has a "black box" that makes the OD operate more like a 7-speed transmission, or a 6-speed, depending on if it's set up on 2nd gear or not... some "hot" modified engines should avoid using OD on 2nd gear.
The gearbox and the OD "share" the same oil. Most often I've seen 20W50 Valvoline Racing Oil (non-detergent) recommended. But, because the gearbox and OD share oil, it's wise to have both rebuilt at the same time, so that gunk and shavings from one don't contaminate the other.
Other key things you need to know include how to adjust the solenoid to properly engage the A-type OD. Incorrectly set it will quickly burn itself up. There is an a hole in a lever on the opposite side of the OD, that is aligned with a hole in the case when adjustment is correct. Still, I think that's a bit rough and prefer to use a dial test indicator on the release valve, to set it more accurately.
Hope this helps!
Alan