Adaptor with internal thread and mention of rollers indicates the superior (compared to earlier 6 Spring) Triumph 4 Spring Clutch.
With both clutch types it is essential the mating tapers are correct, and blued up a la Bergs is a good ruse. A dab of grinding paste to lap them was an old trick, The drive is carried by the tapers, not the key....make sure this locates and does not foul the adaptor.* Too loose on the nut will shear the key and often damages its location in the mainshaft. This is of no real consequence, but as mentioned tab washer is more often ineffective, loctite and a clutch locking plate, breaker bar or rattle gun to get that centre nut good'n tight should do it.
A clutch centre extractor should be required to remove a correctly assembled centre. From experience make sure the adaptor will fit the extractor before assembly. The threads on both may need a fettle, easier to do on the bench.
Swarfy.
* Additional. See further later comment about the key by CB...That's what I meant to say! Pattern parts are notorious for being not quite correct, hence care needed to ensure the tapers match.