I have been unable to complete this mission due to the fact that for me NPC Chancellor J'mpok is no longer available. I have attempted communication with everyone in the Great Hall with no success. When I started the game the Tutorial missions were not available for some reason and I only recently discovered them. If it matters, I would suggest that NPC Chancellor L'rell take his place when J'mpok is no longer available.
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See this post for a workaround.
https://www.arcgames.com/en/forums/startrekonline#/discussion/1272025/cant-finish-or-drop-mission-npc-unavailable
Have a look in the "Warzone" story arc and play "The House Always Wins".
There is a section inside the Great Hall at the end of the mission. Play it through but don't beam out. You'll then be able to progress your Qo'noS tutorial.