You can find out the information you want without asking "How do you like the Director?"

For example, you can ask:

How does the Director support the organization? How do they support their reports? Have you seen them "go to bat" for the org (or someone in the org)? What did they do?

How long has the Director been leading the organization? How long have the senior leads been in the organization?

Are longer tenured people sticking around, or are they moving on to somewhere else? Etc.

Don't ask if the Director is good. Look for the artifacts of having a good Director.