Multiple realities(covers information from several alternate timelines)
The Office of the Admiralty was an agency within Starfleet Command responsible for the administration of Starfleet.
In 2267, while pretending to be his mirror universe counterpart, Kirk was asked by "Captain's woman" Marlena Moreau how far his ambitions extended. Was his scheming part of an effort of advancing to the Admiralty, or even further to the cabinet? (TOS: "Mirror, Mirror")
In late 2375, the Admiralty requested and required that Captain Benjamin Sisko take command of the USS Sao Paulo. This order was signed by Vice Admiral William Ross. (DS9: "The Dogs of War")