In a director's position you have the title of boss, but that doesn't guarantee respect among your staff. Being a new director you'll still have t give and gain respect among the staff, especially when bringing new ideas to the center. Sometimes people get stuck in their own ways and believe that things should stay the way they are.

The interviewer wants to know how you will bring new ideas to the table and helping your staff accept the idea. There are different ways that people can introduce ideas to a group, sometimes people approach this by letting everything share an idea, so that everyone is heard. Another way is to try an idea on a test trial.