So, is there a way to prove that someone is a sanctioned psyker? I know many look like it (hollow, lifeless eyes, maybe warmed over death, perhaps missing their teeth, or hair), but is there a legitimate way to tell? The records keeping of the Imperium is as arcane, byzantine, and full of dead ends as every other facet of the organization, and I often see getting info reliably from any other world, certainly sector, as problematic, at best (no dedicated Internet), so asking Holy Terra if this psyker came through their program seems unlikely. If your crew found a young psyker, living on the streets of Footfall, or among the populations of numerous worlds that don't pay official tithes to the Imperium, and they decided to scoop him up, would anyone be the wiser? I doubt there's any identifying tattoo, as much as I doubt one couldn't fake it, if it did exist. I see plenty of Inquisitors who are psykers, and none of them have the harrowed look of a sanctioned psyker, even having seen all the additional things that should unhinge even an Inquisitor's mind. How might you be found out? That might be the work of rejuvenants, or surgeries, but a Rogue Trader could afford those, too, if they were of a mind, leaving some to question if the individual has been tested.
If you did pick one such psyker up, and you happened to have an astropath, or some such, aboard your ship, who might be as loose with his organization's rules as many other individuals who also serve a Rogue Trader, could they "test" this new acquisition? They've been through everything, so they have some idea what to look for, if they don't just flip, and say "we must report this psyker to the Black Ships!"
While I know that the Imperium is very grimdark, and many petty crimes might be punishable by death, just because the Imperium can't afford to be less severe, what would the actual fine/punishment be, to the Rogue Trader, for making use of an unsanctioned psyker, assuming it is discovered prior to that psyker, intentionally, or otherwise, starting a calamity psykers are feared and reviled for being able to cause?
As a last bit, if your ship found itself without any astropaths, say something went pear-shaped, on the last run, what might be the official means of resupplying this particular resource?
Kind of curious about all this because, if say one of your group's members had a kid, in game, and they developed the psyker gene, it might not be convenient to have to send them off to Holy Terra, wait forever for them to arrive there, wait 10-30 more years for the training to conclude, hope that they survive that, and then maybe get them back, if you grease enough cogs. If you just said "screw it! Way out here, beyond most of the Emperor's sight, who'll know? And besides, Ostius can look after them, for that aspect. He's a great, old guy, as astropaths go, and definitely been through the whole song and dance about what it means to be a psyker. It'll be like he has a grandson!" If the kid doesn't make civilians have stray nosebleeds, or blizzardy winds, out of the blue, are they likely to be caught, and can the great power of their RT benefactor shield them?