On many job applications you'll see a question like this: When you've completed all your assigned tasks, what will you do next? Ask your boss for more work, find something to do, or do nothing? If any of those answers are wrong, it's the do nothing one.
Yes, if you've completed all your tasks you should probably ask your supervisor what she would like you to do. That's acceptable some of the time, but in certain positions, whether that's creative or idea-making, you need to be somewhat self-driven.
If you are a "Director of X" or "Lead Something" there needs to be an element of discovery and drive. If you have to always be told exactly what to do, it will appear as though you're laking some creativity and self-motivation. "Find something to do" has a negative connotation, but many times, if used well, those times of "finding" may pay off and show your enthusiasm for something new.