Were you playing in my Traveller game, once you finish your Prior History we would sit down and try to flesh out what your character actually did to earn his position (if any), promotions (if any), and decorations (if any). For example, a 7-term Navy character who ends up O6 is listed as "Admiral," and let's say the character got an MCUF and a MCG during generation.
Aside: Yes, I know that it's highly unlikely that you can get to Admiral in 7 terms.
The MCUF came in term 3, and happened to coincide with the promotion to Lt. Cmdr., so I as GM might say that the destroyer (DD) the character was serving aboard took significant damage and the character found himself in command as a Lieutenant and managed not only to save the ship but also kill the Zhodani frigates that were swarming around the DD.
After his promotion to Lt. Cmdr., he stayed at that rank for term 4, so let's assume he was serving as XO aboard a bigger ship (CL, say) to size up the potential he showed under fire.
Term 5 he was promoted to full Cmdr., and given command of his own tin can (DD again). During that term, his ship was destroyed! (Wounded.) And he also gained the MCG at the same time, so the DD took some ships with it when it went. Say, his ship saved the merchant convoy while crippling or destroying several pirate ships, or something like that.
Following that, he was promoted to Captain (O5) and then Admiral (06) and retired after seven terms.
IMTU, with a nod toward the Honor Harrington system, there are Captain, J.G., and full Captain ranks. These are the "O5" possibilities. Above that, there are Commodore (basically a permanent Fleet Captain designation), Rear Admiral (squadron), Vice Admiral (division), Admiral (fleet command; subsector-level generally), Sector Admiral, Fleet Admiral (commanding multiple sectors; I do not use Domains but if I did that'd be this guy), and Grand Admiral (overall Imperial Navy command; when vacant this is the Emperor himself, which is a tradition that goes back to Plankwell's time).
The character I outlined above would probably be a Commodore or Rear Admiral, and I'd work with the player to determine what final rank was achieved and what types of ships the character commanded. Squadrons of DDs would be Commodore, while CruRons would be Rear Admiral, for example.
Non-command trees also exist - for example, there is a Fleet Admiral of Engineering who is in command of R&D for the Navy, and there's also a Fleet Admiral of Logistics, which includes medical matters. These admirals don't generally command actual units, but set and review policy, etc.