Ever since Neil Hartman and his uncle tried to instigate an attack on the academy and failed, Lucille sent them back to the human kingdom for King Edward to decide what to do with them.
In the end, King Edward gave his verdict, and now Neil, his uncle, and all the other mercenaries were ordered to live in the monk temple up in the mountains until Nordrassil had been found.
Meanwhile, Neil was asked to make a choice between returning to the academy and joining his uncle in the temple, but he chose to be with his uncle and everyone else. This meant that he wouldn't be able to return to the academy anymore, and someone else's rank would have to be upgraded to the new number ten of the academy.
Adrian was the one who became the new number ten because he was initially ranked right below Neil.