I was invited into a fleet on ESD and got promoted to fleet leader (in this fleet, everyone is a fleet leader). One of the first things I tried to do is visit the fleet starbase in Eta Edriani. However when I clicked on "Approach Your Starbase", nothing happens.
Another related issue is the fleet-related PvE queues "Federation Starbase Blockade" and "Federation Fleet Alert". While I could join the two queues and the dialog to join the action pops up when there were sufficient players in the queue. But when I click "Engage", nothing happens. The 30 seconds countdown stopped at around 15 seconds, which I took to mean enough players have engaged the challenge, but I was not launched into the challenge map itself. Further attempts to re-join the queue fails with "you are already in the queue" and the option to leave the queue is greyed out.
Logging out of the game and logging back in fixed all the above issues.