Ok, I'd probably ask what things s/he thinks s/he can improve upon, and how you as parents can help with that.
Do you know why the previous HT left - was it a simple case of retirement, for example, or was there something else? If something else, then challenge this new HT on that - there's always going to be a period of slight unsettlement after one head leaves and another joins, and obviously you'd want this new HT to remain in post long enough not to cause too much turbulence for your child.
Also ask things about the new GCSEs - how does s/he intend to prepare this new cohort of students for the new, tougher GCSEs. Has what they've done so far worked, or does some improvement need to be evidenced?
And finally, the one thing that every parent wants to know - how does the school deal with bullying? (And beware the HT that says there isn't any!).
Good luck. We have similar in our area, except school is 'Requires Improvement'. So our questions are basically going to be 'How do you intent to improve?!'.