Royal Enforcement Division

Introduction
Royal Enforcement Division or RED has a literally translated meaning of: Zahard + Royal(ty) + under direct command + punishment/enforcement + squad/division/regiment/etc which gives some hints about what they do.

This division is part of the Zahard Family. However, the members of RED are likely not considered Zahard's sons or daughters. This is evident from the fact Ren doesn't bear the surname of Zahard.

The division is infamous even among the Zahard Family and apparently, Ren was called "an assassin of the Zahard Family" (Ch 71).

It has been noted that they may be able to recruit people for the Zahard Empire, as Ren stated that Baam might be worthy of bearing their crest.

They serve Zahard and no one else. However, the division is not loyal to him. The amount of loyalty towards Zahard among the individual members varies greatly as most of them joined the division only to fulfill their urges and lust to commit murder or to fight. Or if not, to aid their Family's ambitions(like Bia Family). The only thing the members have in common is that they are all in awe of the power of Zahard.

Their scope of authority
Note #1: that the below content is framed from real-life context derived from here: "miliary police versus officials"(likely, South Korean Military Police versus military officers)(Ch 68)

Note #2: Their authority likely doesn't extend to Palace personnel like courtiers, cooks, etc. If there is any crime committed by a Princess involving anyone who isn't from the Zahard Family, it's currently unknown who they team up with. It could be another Princess, civilian Police or another authority.

The RED are like a Military Police(South Korean) division within the Zahard Family and they uphold the applicable Laws binding the Princess and enforce discipline of the Princess in terms of acceptable conduct within and outside of the Palace.

This includes duties a Princess might be tasked with, who she may or may not associate with, her interactions with and in front of the general populace, ensuring she doesn't attack anyone she has no authority to(Eurasia Enne Zahard attacked or killed random people who she had no authority to), the Rules governing all Princesses, the 13 Month Series rules governing a formal Princess who has accepted 1, etc.

They have the authority to conduct surveillance of a Princess' behavior, to act on their suspicions(possibly permission from a superior is required), to investigate the reasons behind her breach of rules and collect evidence(circumstantial, concrete) of her misdeeds. All these information are then transmited or handed over to their superior who will decide whether they should continue the investigation, inform the King or to ignore the offences for now. In addition, the RED member has the authority to ignore a Princess' offenses, should he decide so(ch 70).

Take note that like all military personnel, a Princess likely has to obtain permission from a higher authority like an older Princess or most likely, the King if she wants to take an extended leave. If she hasn’t reported back to the Palace for a certain amount of time, hasn’t made any contact with anyone and all attempts to contact her Pocket fail, it can be viewed as Absence Without Official Leave(AWOL) and it means she has gone missing or rather, deserted from the Palace. And when the King finds out, he then issues an order to the RED which then tasks a member with finding the reasons behind her disappearance. Like the Military Police, the RED might also be tasked with preventing a Princess from deserting the Palace.

In the event that a RED member fails to complete a task, it seems they can make a report to their division and/or the King as long as there is evidence(Ch 72).

Like the Korean Military Police, it is possible they may guard and escort a Princess who has been declared a criminal and also, provide infantry field support for a Princess on certain missions.

Since the Palace isn't a military installation and the RED isn't an actual Military Police, it's likely the Royal Palace guard it instead.

Orders and Missions
Take note that the King issues an order to the RED which in turn, reviews his order and related information. A mission is then issued to a RED member. Over time, the scope of that mission might be revised and even expanded, like how police investigations eventually evolve.

Below is an example of a mission(Ren's mission on 2nd Floor):

The King issued orders to retrieve the Green April(ch 70) which the RED interpreted to include eliminating Anak Zahard. Since it's unlikely the RED and anyone(excepting Yuri Zahard, Evan Edrok, Headon and Baam knew the Princess had lost her Black March, it's more likely Ren somehow found out Anak was holding the 13 Month Series either from gossiping with Quant or Lero-Ro or from observing her, using the security system implemented all over the the 2nd Floor in the dormitories and even testing facilities.

He must have heard about the "skirmish" between Androssi and Anak from Hax and then, decided to expand his surveillance to include Androssi. And after his contact with his superior, was given orders to his mission was expanded to retrieving the Black March and likely, given permission to continue observing both of them.

In addition, the Black March itself was evidence of Yuri Zahard's breaking of the 13 Month Rules. However, she managed to kill his container body and retrieve the Black March as well as the Green April. With no evidence left, Ren's mission was a failure.

Hierarchy and structure
The Enforcement Division has independent ranks and a command hierarchy. This was evidenced by the fact that Ren was talking to his "sunbae" aka his superiors in Ch 54. He also mentioned a "Vice commander".

Ren is No. 67 of the division.

Symbol used by the RED
Members of the division bear a crest similar to that of the Crimson Three Eyes seen on the right. This is likely to dispel confusion, in the event a government official is serving a RED female member and a Princess whom he's unfamiliar with, as only some Princesses are known among the citizens of the Tower.

However, the crest may or may not be also named the Crest of the Crimson Three Eyes.

A symbol similar to The Crest of The Crimson Three Eyes appeares on a wall of the cave that Baam was trapped in his entire life. (Chapter 28)