The Voyage of the Resplendent by Philip Douglas

For centuries the Empire has been ruled by successive clone daughters of its founder with a mix of military might, political manipulation and a total monopoly on faster-than-light travel. That control has now faltered, systems are in open rebellion and the Imperatrix is fighting for her throne.

You are Johanna Waechter, police officer and captain of the Resplendent, and your job is to keep the peace in the parts of the empire that still has some. That is going to be about as difficult as it sounds.