Well, not knowing anything about the school and its Greek system, here are some questions that may or may not apply to the the campus where you're interviewing. Also, are you applying for Director of Greek Life, or some other position, such as Graduate Assistant to the Director of Greek Life?
-Our campus has a very diverse Greek system, consisting of various groups that haven't always interacted as much as they could. What are some ideas you might implement to promote unity among all the Greeks?
-What do you feel are the most important risk management issues facing chapters, and how do you feel you would handle those issues?
-Our campus holds NPC formal recruitment in the fall, but some other schools in this area have switched to spring recruitment. What do you think are the advantages and disadvantages of spring recruitment?
-What are some ways you might motivate the Greeks, both as chapters and as individual members, to focus on academics?
-What are some lessons you learned as a collegiate Greek that you could apply to a role as a university official managing a Greek system?
-The Greek system here at our college is a lot [bigger, smaller] than where you went to school. What are the similarities and differences you see between a small and a large Greek system?