The Council of Elrond replaces the High Lords of Terra. Do they do a better job?
No prep. They learn on the job.
Gimli son of Gloin would make for a very effective representative for Mars. Stubborn, bellicose yet nevertheless capable of steadfast support to his factional foes & erstwhile friends. He could balance the Mechanicus's desire to hoard STCs with the need to actually cultivate alliances with the Imperium's departments.
Boromir for the head of the Administratum, easily. The Captain of Gondor would make for an inspiring and rejuvenating force in Imperial governance, and would likely be the nucleus of an Imperial rennaisance as he leads a new crusade into the east against the tyranids and chaos. Thematically, it would be appropriate if he ended up dying due to some Inquisitorial intrigue after they suspect he was flirting with the radical idea of using chaos to defend humanity.
Aragorn for the master of the Inquisition. His knowledge of many languages, how to be sneaky, blend into all societies (he is equally at place in a dingy inn at Bree or in the highest halls of Gondor or Lothlorien), close quarters combat & experience fighting fell sorcery or armies of the dead mark his as competent for the role. Most of all, he is objective-driven and lacks the complete compassion Boromir has which could lead to damnation or hesitation. Aragorn is always driving the party onwards if it means the destruction of Sauron and the restoration of Arnor. He is likewise ambitious yet immune to the temptations of power. The only issue he has is the Ordo Xenos might look a bit askance at his marriage with an Eldar who became a human.
Gandalf I'd completely typecast as the head of the Astronomicon. It's the only place I think Gandalf could be placed where he wouldn't cause loads of damage; his power works against him in 40k because chaos is corruptive like the ring.
Elrond would make a fine fit for being in charge of the Psykers. A powerful psyker like himself who can see the future, resist evil and has a nurturing personality would have a very positive effect on an institution charged with nurturing humanity's latent psyker abilities into something which is safe and useful.
Samwise Gamgee for head of the Officio Assassinorium. Don't fuck with
SAMI'd put Pippin in charge of the Ecclesiarchy. Just because it would be funny, and the Ecclesiarchy is already dysfunctional so putting Pippin in charge would just make it a different kind of dysfunctional. I guess on a more serious note Pippin is an inspirational leader, successfully rousing the Shire against Saruman's remnants so he could pull off a great demagogue.
Legolas and Glorfindel for High Admiral and Lord Militant of the Guard respectively. Having two steadfast commanders and warriors in charge would help the two most powerful armed factions in the Imperium represent themselves confidently in the face of the other's personalities; they'd also be stiff enough to resist any lobbying pressure from their own powerful subordinates.
Frodo and Bilbo can be in charge of the Navigators. Their unparalleled charting and journeying could do them fine there as liaison for the navigators; their non-judgemental personalities and ability to make friends of hostile mutant hobbits would serve them well when representing hostile mutant humans.
Merry for the Arbites. Merry is an MVP who stiffens the resolve of everyone around him. Through his actions and words Theoden is roused from despair and Eowyn slaughters the Witch King of Angmar. If the Arbites started acting more like Merry you'd see a lot more outreach to the underhive and a lot less paramilitary invasions of the underhive. Being able to tap into the latent courage of all of the Imperium would be a great boon to their forces - I'm reminded of one short story where a tyranid invasion started stalling when it squared off against the gangers of the underhive.