Hey, I'm a relatively new GM so bear over with me on various mistakes i make

I'm currently running a campaign with some of the starter adventures and while running "Illumination" the psyker of the group, picked up the last tarot card when the Daemon died.

He hasn't reported this tarot card as being found and plans on keeping it (I'm thinking)

Now we are running "Purge the unclean" we are in the first part of "rejoice for you are true"

I got them pretty well introduced to the task at hand, without the card being part of the solution.

So now my question is to you, other more experienced players then me, how do I punish him for keeping this card?

I was thinking something about the events that happened with Aristarchus should be somewhat replicated, and force the Daemon to corrupt his mind.

How would you guys play this out... or do you have any other ideas.

Anything is very welcome.

This is what I would do were I in your situation as a gamemaster:

Nothing. At least for the first few game sessions. Let the players forget about the card or if they try to interact with it or use it in any way then nothing happens. Let them "stumble" across some other bit of technology that gives them hints towards the events of Rejoice.

But when the players start to get on a roll have something go wrong at an inopportune time. Nothing drastic but something like a guard walking his route early or a random rainstorm when they are climbing rooftops (or running around on Ambulon!). Increase the frequency of these events slowly and then start having the card effect things. Headaches when around it, Machine spirits going crazy. Animals freak out. The tech behind the card is unfathomable and the players should really get the point that it's bad juju. Turn it into a "bad guy" or even "THE bad guy". When I ran Purge the Unclean the final homebrowed tie-up session was to find a radical demon-binding Inquisitor leader of the Serrated Query and their own recently-gone-radical-while-chasing-the-radical-Inquisitor-boss-Inquisitor and destroy them both. This lead to a showdown on a cathedral planet where the "bad" radical Inquisitor was using a Logos Daemonis (Creatures Anathema) and the "good" radical Inquisitor was using a Halo device. Needless to say the planet required Exterminatus when all was said and done...

But I digress. My point is the card could easily turn into something like the Logos Daemonis or worse... or even be a dud in the end. I say let the players sort it out for you by putting it on the back burner for now to see how they progress through Rejoice and wait for the perfect time to strike with it. My players thought using another player character's body to summon and bind a demon was a good idea. Turned out it wasn't.

Hmm I like the idea of the card sort of being a catalyst for bad things to happen, or worsen situations that would fit it.

It also gives me a way of using it without having a player in my group becoming possessed by a daemon. (They are also new to the universe)

I'd love to hear other ideas still, since as Rumil pointed out, I should prolly let them forget about it for a bit

Once, I had a player roll a d6 between 1 and 3 times per session, every session for about 4 months. We played a couple of times a week.
He panicked so much as paranoia set in. Far more horrific than anything I could have inflicted upon him.

Having said that, In my current game, a player pissed off a (custom) daemon which is now stalking him in the shadows. He gets itchy if he stays in one place to long as tho something shadowy is behind him, getting closer. This is worse in combat and the Daemon is empowered by the raw emotions of the fight. He gains +1 WS per round of combat as he is more and more desperate to finish the fight so he can move on (I dont need to impose any reckless behavior tests as he usually charges the biggest thing in the fight in the first round anyway)
However, the real trick is that one of the party has the 'From Beyond' trait, so he can see a growing shadow looming over his comrade. So I dont need to do anything, I just let the players work it out how they see fit =P Yes, I am a lazy DM

He should definitely be hearing the daemon's whispers (promising him power or urging him to make a Dark Pact), be dreaming about the daemon…and hey, let the card give him some extra power with divination-type powers. Chaos is appealing because it does give you power to follow it, at the cost of your soul. Inflict Corruption - or keep a tally of it in secret and inflict it on him at appropriate times or when he finally gets rid of the card, and don't let him metagame his way out of getting rid of it as he gains corruption from its presence - power corrupts, after all, and allowing the OOC infliction of corruption to give him an IC clue to stop carrying the thing breaks immersion.