Just had a way for it to make sense:

Disguise. The guards aren't aggro to everyone, just criminals. So maybe the edge represents a character's ability to disguise himself.

Some other perks you could add: ability to purchase goods from town merchants who normally don't sell to criminals. Ability to enter the Inn of the Eternal Star while wanted.

You'd have to make "more powerful" guard mobs see through it, though. Or maybe have it not work while the criminal's adrenaline is high. Otherwise it seems like too powerful an effect for a single edge.