The chief does not have the ability to undercut her boss with impunity. This would fall under the heading of insubordination. She should have been fired.
Let's hope the mayor has some asbestos underpants, as they will be coming for him.
Usually the City Police Chief is changed when mayors are changed, they are mayor appointees. Especially if the party in charge changes. Even then that is not a reliable fact, the mayor will want his OWN crony in the position. They are trying to make it a sexual orientation one to stop the change the mayor wants.
A county Sheriff Chief is usually elected.