New Order

New Order was the Quirk that was formerly used by Cathleen Bate, until it was stolen from her by Tomura Shigaraki. It is now possessed by neither, following its self-destruction.

Description
New Order allowed the user to set a rule onto their surroundings, allowing them to manipulate and bestow new properties onto themselves and the world around them. This can range from simple descriptions to more conditional ones based on cause-and-effect. Cathleen could give herself additional abilities, as well as manipulate the condition of her opponent's body. She could even use her power on incorporeal things, like the air and laser beams.

It is described as a power that redefines what a Quirk can be.

Weaknesses
In order for New Order to activate, Cathleen needed to both touch the target and say its name. However, when targeting a living being with a sense of self, Cathleen's understanding of the target's identity had to align with their own. This is shown when Tomura Shigaraki's heart didn't stop when he moved, due to even him questioning his true identity, as either Tomura, All For One, or "Tenko". Because of this, inanimate objects are much easier targets to set rules on, as without a sense of self, Cathleen's one-sided understanding of it is enough to enforce the rule.

The effects granted by New Order were not omnipotent, as there are limits to how great they become. There was also a hard limit on how strong Cathleen could make herself with her Quirk, and she could not use it to become all-powerful or invincible. She could also only impose two rules at any given time, so if she decided to implement a new rule, one of the previous rules had to be disengaged. Furthermore, a rule couldn't arbitrarily effect another target she hadn't touched through clever wording (i.e. after she touches the air, making it so that someone who also touches the air will die).

Due to Cathleen setting a rule that New Order would revolt against other Quirks, New Order acted like a virus within the body of Tomura, purging several of his Quirks, making him unable to use it or any other Quirk while he explodes from the inside out. This eventually resulted in New Order's self-destruction, which left Tomura in an injured state with his Quirk Factors damaged.

Usage
Cathleen constantly kept one rule active, which allowed her to grant herself superhuman physical characteristics (i.e., super strength, super speed, super durability, etc.), meaning that her physical aptitude was similar to, but still considerably weaker than, All Might was in his prime. In her battle against "Tomura", she used her Quirk to remove all the air one hundred meters in front of her (around "Tomura"), forcing him to hold his breath, as well as to safely catch a laser that was reflected back towards her. In more desperate situations, Cathleen disengaged her constant rule of superhuman physical characteristics. This allowed her to use Super Moves with two rules, but subsequently made her more vulnerable and physically weaker.

When "Tomura" succeeded in stealing New Order, Cathleen used one last rule in order to stop his Decay from killing her, which only ended up delaying it by reaching the limit of how strong her body can become. She also secretly declared another rule on New Order itself, causing it to revolt against other Quirks, resulting in a vestige of Cathleen tearing apart Tomura, All For One, and the vestiges of the stolen Quirks, even destroying several of them, as well as causing Tomura's physical body to rupture.

Trivia

 * New Order's name may be a reference to the Latin phrase  ("New order of the ages"), which is used as a motto on the reverse side of the.
 * When using New Order in the manga, the user is shown to have striped speech bubbles that resemble the American flag.