Issei is initially presented as the student council president and part of class 2-C during the preliminaries. As part of the council's job of enforcing school rules, he is performing inspections on students as they enter.
Hakuno realizes that Issei performs the inspections even if no one is standing in front of him. He will act as if he is talking to a well-behaved student.
Following the preliminaries, he, along with the student council members, ensure the Holy Grail War runs smoothly. In Fate/Extra, he is usually found on the third floor.