GC rank up

Hello i'm currently Maelstrom/Storm Sergeant First Class and it says I have to get authority from the npc to the right (same guy who gives chocobo quest). Now i'm level 37 and his next quest is level 44. Do i need to finish that to get the last sergeant rank and then the new tier of lietenant?

Thanks!

Yes you have to get 44 to get the final sergeant rank, to get lieutenant however you are going to have to beat the main storyline.