The Red Police functioned as a militia force on Prakith when Foga Brill ruled, having transformed from a Moff into a Warlord.
One of their roles was to protect the families residing on Prakith whose members were forced to join the Grand Imperial Navy. It's also possible they carried out the large-scale killings of vagrants without homes, which were rumored to occur in certain urban zones of the planet.
It's possible the warlord created them as a way to restructure his sector group to consolidate control, or they could have existed before, back when Prakith was a loyal Imperial fortress world.
The Red Police could have been a nod to the red-armored Coruscant Guards that were made for the Star Wars: Shadows of the Empire multimedia project. These guards appeared in the same year as Shield of Lies, and were reported to have served on several Core Worlds.