I spoke with the NPC Storm Personnel Officer and chose Apply for promotion. He says to qualify for next promotion to complete a trial and finish rank 2 in the hunting log for the grand company. He then says I have not completed the trial and to speak to the storm commander to receive the trial.
By this point I had already spoken with and received the quest from the NPC R'ashaht Rhiki <Storm Commander>. After receiving the quest to complete Dzemael Darkhold I completed the Duty multiple times. I tried to turn in the quest after each time I completed the duty but it would not allow me to.
In my journal it says the quest is complete yet I do not have access to the 3rd rank enemies in the Maelstrom hunting log and I am stuck as a Chief Storm Sergeant.