General:
* Power
* Control
* Influence
* Command
* Jurisdiction
* Rule
* Sovereignty
* Leadership
* Expertise
* Prestige
Specific:
* Expert: For someone who is an authority on a subject.
* Official: For someone in a position of authority.
* Government: For a governing body.
* Source: For a reliable source of information.
* Master: For someone who has complete control.
More informal:
* Boss
* Big shot
* Heavyweight
* The man
The best synonym will depend on the specific meaning you want to convey.