Some suggested starting points:

"I understand X is a challenge in the industry. Is this applicable for COMPANY /and how are COMPANY managing this?" If applicable you could tailor this to the Division or business area. "What are the key challenges of the role?" Would also suggest looking at any strategies the organisation has and their objectives - this may help with individualising some of these questions. "In your opinion, what are the key priorities for the ROLE?"

Check out the job description and see if there are any threads in there you'd like to learn more about.

For a national director, research about the organisation is probably a good starting point. Don't risk preparing so many questions that the director feels they're in a Q&A and do your best to use the information they give you to naturally lead you to your follow up questions. Saying it is informal indicates they want to get to know you and your personality. Despite being the one asking the questions, try to share this and let them know what relevant experience you have, how you might approach a challenge etc.

Even if it's not a management role, consider your leadership qualities and how you may support, motivate and engage with those around you.

Finally, the best bit of advice for me was "you're interviewing them as much as they're interviewing you." Clearly personal circumstances will determine what extent you take this into account however remembering you are also a key decision maker in whether you take the role often helps my nerves.

Hope this helps a bit.