Clarence exited the bar shortly after the conflict was resolved and went back to his inn. He couldn't afford to wait as he had very little time before the ruin finally stabilized and the academy took the cadets participating into the ruin. He would miss the timing if he uselessly wasted time.
Entering his room, he took out a different mask from his spatial bracelet and switched it for the current one on his face. It was the one he had prepared as the academy only gave you one.
The masks sold by the academy at least had credibility as they would save you from being discovered from anyone below rank seven. They were just perfect for this mission. It was similarly costly so Clarence nearly had to clean his ruin space for the masks and the extra id.