how long does it take for a psyker to grow an arm back if they activate the psychic power regeneration

As long as the plot needs it to

In my game the Psyker lost his legs due to the Eviscerator-wielding Guardsman being Dominated by a chaos sorceror. The guardsman felt very guilty afterwards, and tried to re-attach the legs with duct-tape. So I ruled the legs would re-attach in a matter of days, conveniently healed by the time they were to start the next phase of the adventure.

But that was when I was still a nice GM, believing my PCs needed a hand (or a few legs, in this case) in order to get by. Today I would have let them carry around the crippled psyker for months, cackling with insane glee all along!

I interpreted it as with the wounds, so if he filled up his wounds-pool and is completly "healthy" again, so is his body complete again. Sort of T-1000 style where you can literally see the flesh flowing and growing as it forms itself into an arm/leg.

If gashes and full bullet wounds can be undone in a second (Close Wounds power), the Regenerate Power should work in the same time-ballpark, aka measured in rounds.