When someone, or some group, assumes and holds authority in practise, without any legal authority to do so.

This is known as "usurpation of authority" or "usurping authority." It occurs when an individual or group takes on a position of power or authority without having the legal or legitimate authority to do so. Usurpation of authority often involves acting as though one has the right to make decisions or enforce rules, even when there is no legal basis for such actions.