I have been asked to post here & submit a bug report as the GM are unable to help.
I am lvl 24 on my alt and I just finnished the Klingon story arc, I got my promotion & new ship however I am unable to start Yesterday's War or any other story arc for that matter. I have tried to talk to the people drectly to start the quest but again nothing. I have found out that it is due to me being OVER the recamended lvl
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https://arcgames.com/en/forums/startrekonline#/discussion/1234823/romulan-mission-an-inside-job-wont-trigger
The short answer; you must first run the current featured episode then normal progression seems to unlock again.