In DS9's Paradise Lost episode (season 04, episode 12), the plot is heavy with Starfleet intrigue: Sisko discovers that Admiral Leyton is plotting to take over control of Earth and put it under a military rule. His options seem limited to convincing the President of the United Federation of Planets of the plot, or convince captains working for Leyton to stop obeying orders.
This raises the question: are there no other admirals that he could have gone for and convinced that Leyton was a traitor? Are there no people of higher rank, fleet admirals maybe? We know that there are many admirals, and presumably a number of those are stationed on Earth, since Starfleet Headquarters are there. Why aren't we seeing any?
This makes me wonder about a broader question: how does Starfleet governance works at the highest levels of the hierarchy? There seems to be a commander in chief (e.g. in season 1 of Picard, Fleet Admiral Clancy seems to hold that position?), but who appoints/elects them, how long is their term, and are there mechanisms for their early removal?