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 as they weren't chosen by the King to become his "adopted children". This is evident from the fact Ren doesn't bear the surname of Zahard but the surname of Bia.

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

Symbol used by the RED
Members of the division bear a crest similar to that of the Crimson Three Eyes seen on the right. Like any symbol used by an army division, this is probably separate and distinctive from the Zahard symbol depicted on items the Princesses wear.

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

It is possible the RED members receive the items bearing their symbol from the Commander, instead of the King.

Hierarchy and structure
The Enforcement Division has independent ranks and a command hierarchy. It's possible only the top ranks are appointed by the King while the rest of the members are recruited. Ren showed intention of recruiting Baam(ch 54) when he'd become a Ranker but this was before the boy was revealed as an Irregular.

Known ranks: Commander, Vice commander(there might be more than just 1).

Ren is No. 67 of the division and the youngest in terms of rank. This implies there're likely 67 ranks.

Loyalty to the King
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.

In addition, they join to further their personal agenda or their Family's ambitions. For example: Ren attempted to place Androssi into a predicament so she would lose some favour with the King while the Princess of the Bia Family would benefit if he succeeded in gaining proof of her "misdeeds". Many or all of the members will do anything to fulfill their agendas and to gain favour with the King, so they will attempt to complete the mission. So, their loyalty doesn't matter.

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: Since the Palace isn't a military installation or a place under military command and the RED isn't the actual Military Police unit, their authority likely doesn't extend to Palace personnel like courtiers, cooks, etc.

Note #2: If there is any crime committed by a Princess involving anyone who isn't from the Zahard Family, it's possible there could be a joint investigation consisting of RED members and another party like a few Princesses, the 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 Zahard Family. 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.

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).

It is possible they may guard and escort a Princess who has been declared a criminal and also, provide support for a Princess on certain missions.

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.

For certain orders, the King doesn't care who completes them and how they were carried out. His only concern is the end result and the King was said to be "very happy" with Yuri Zahard, who retrieved the Green April 5 years ago(Ch 80).

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.