Legion Consuls or Consul-Opsequiari (Consul of compliance) were basically Space Marine Military Police. Several Legions used them, most notably the VI Legion before Russ was found and the IX Legion after the finding of Sanguinius. These guys worked in the same manner as Commissars, in that if anyone disobeyed their orders they got *BLAMMED*. But unlike regular humans Space Marines don't need to be "coaxed" into fighting. Instead, the Consuls were there to make sure the marines did not go the extra mile. Two Legions were noted for their use of these guys, the XII Legion and VI Legion. It has been argued, in the fluff, that the Wolves needed them more than the Hounds since the Wolves got all choppy when their enemy up and ran. So the 6th Legion was more like murderous nut-jobs than murderous assholes. It was said that when the 6th was deployed to the world of Moloria, they would have killed everything had it not been for the Legion Consul's who had to *BLAM* a bunch for trying to kill everyone. Once Leman Russ was found, it seems these guys were dissolved. Since they were often recruited from veterans of the same Legion they were from, they were probably re-integrated back into the main Legion structure. Surprisingly they are never mentioned after this. Ever. Even when discussing the World Eaters or their habits.
The Chaplain could be said to be their spiritual descendant.
The Burning Eyes
Also known as the Ofanim, they were the secret agents of Sanguinius, tasked with quietly killing any Blood Angels that fell to the Red Thirst and silencing any witnesses. Described as "wielding weapons considered unworthy of true warriors", they're clearly a cross between Field Police and Moritats, while their name is a reference to the angels of the same name in the Christian and Jewish beliefs, which were burning cartwheels of fire with many eyes.
In modern 40k their roll has practically been taken over by Astorath and the normal Chaplains, as happened with regular Field Police.
Back in Rogue Trader Space Marines had "Field Police". They also had Medics but that was then. In a flash of intelligence and record keeping, Forge World has included these guys back into the fluff of the new Horus Heresy books. But only on one page in Inferno. However, their icon is the same as the old Field Police from RT.
They lack any particular rules, though the term 'Consul' is used by Forge World...as a general term for Legion Centurions with a specific specialty. If FW were to retroactively give Consuls rules, they'd need a newer, spiffier name, and that's if they even bother to say that they still exist. Odds are that they were an early Crusade holdover and were dissolved once the Primarchs reorganized their legions.