Below are an initial draft of rules for using the Adeptus Arbites in your games of Warhammer 40,000: Kill Team. I've drawn upon the 3rd (? - 1999) edition Warhammer 40,000 rules for the Adeptus Arbites that appeared in issue 29 of the Citadel Journal and the 2nd edition Necromunda rules for Enforcers, as well as both editions of Fantasy Flight Games Dark Heresy RPG (especially The Book of Judgment), the Inquisitor game, and online research at Lexicanum and the 40K Wikia. It should also be noted that later editions of Warhammer 40,000 have included rules for representing the Adeptus Arbites, usually through the rules for [Inquisitorial] Stormtroopers and the Imperial Guard/Astra Militarum (equipping models with shotguns and using certain doctrines).
One principle I've drawn upon is the rules being limited to the options in the box. However, there were two ranges of models. The first were the 2nd edition Adeptus Arbites models and the second were the Necromunda Enforcers models. So there's a little wiggle room.
Adeptus Arbites models:
Page 1 (introduction)
(Pages 2-4 are a work in progress, and none affect actual rules, so I've omitted them for now.)
Page 5 (Crowd Control Grenade rules, Adeptus Arbites faction tactics)
Page 6 (Adeptus Arbites kill team options)
Page 7 (Adeptus Arbites weapons, equipment, and costs)
Page 8 (Adeptus Arbites commander option)
I've used the Tempestor Scions rules as a baseline. Most of the weapons/wargear had rules in other factions (including Genestealer Cults), so the only ones that have had to be created are those in red text. As much as possible, I drew upon the Necromunda Enforcer rules.
The Crowd Control Grenades rule is sort of an experiment, and I'm not certain about it. I didn't want to use Voice of Command as that would have just made the Adeptus Arbites into Astra Militarum. When working on the weapons/wargear rules, I found that using the different grenades took too much room, breaking the format example of the official rules. Also, the standard grenade rules in Kill Team are much too simple. Envisioning a riot control situation (which should be pretty common to the Adeptus Arbites), I could see a line of Arbitrators throwing grenades to disorient and disrupt a crowd of rioters (or heretics, or cultists, or whatever). So I decided to see if I could take the 2nd edition Necromunda rules, streamline them a bit (going with only 3 of the possible grenade types), and turn them into a rule unique to the Adeptus Arbites. The first draft was a bit too powerful in my opinion, so I adjusted it by limiting it to one Arbitrator per turn (not counting the Tactic, which came later) and incorporating the randomness of the scatter dice (which don't exist in Kill Team) by allowing the opponent to move the grenade marker a random distance away. Aside from that, the rules for the grenades are fairly faithful to the Necromunda rules (in fact, I think I still need to make some adjustments to get some terminology fixed).
Two of the Tactics are copied from existing factions. I originally had four from Astra Militarum, Genestealer Cults (maybe - I know I looked at them), and T'au, but I removed two when I came up with the two Adeptus Arbites unique Tactics (Crowd Control enhances the Crowd Control Grenades rule and Lockshield represents the Adeptus Arbites locking their shields in a riot control situation). The commander tactic was
Since the Arbitrator stat line is essentially that of the Tempestor Scions, I originally used the same points value. I reduced that by 1, though, when I changed the starting pistol from a bolt pistol to a laspistol (and assigned the bolt pistol a cost of 1). It comes down to the difference between a laspistol, power maul, and crowd control grenades versus a hot-shot lasgun and frag grenades. If playtesting shows that the stock Arbitrator is equal to the stock Tempestor Scion, I'll probably re-adjust (un-adjust?) the costs.
As far as the missing pages go, I'm working on an extensive set of tables for names. Since the Arbitrators are recruited from across the Imperium, members of the same Precinct House might evidence a variety of names. So I'm working on eight tables representing four additional regiments of the Astra Militarum and four "generic" other worlds (using real world names for different areas of our world to get more variety). The problem here is that my old computer crashes when I sit too long on certain websites (usually those with adds), and the various online lists of popular surnames tend to be on such sites. The recommendation for names will also suggest using the Adeptus Astartes name charts. Overall, it wouldn't be inappropriate to use take 1 or 2 names from each of the Imperium faction charts, giving your Adeptus Arbites team diverse names.
And it should be noted that this set of rules is a means to an end. It's part of a larger effort to actually get my Hive of the Dead Project (Last Days of Demaras Tertius and Operation: Manala) moving somewhere in the direction of "complete." I've been adjusting from what you see in those linked topics. The Adeptus Arbites come in as a last stage of the Last Days of Demaras Tertius campaign and lead in to Operation: Manala. Imagine taking a lone Arbitrator, short on ammunition, through a gauntlet of zombies, the intel he has vital to the Imperium's effort against the zombie plague. My concept is to use that as a sort of demo game. But I need to get baseline Adeptus Arbites rules down first. This is where you come in, providing input to improve these rules.