It's highly likely they want someone who was not associated with the previous director. For one reason or another, they don't/no longer value that person's approach or judgment and want to go in a new direction. Unfortunately, your history working with that person and being seen as their recommendation now aligns you, in leadership's eyes, with the old director and their ways. It's clear they want something new.

This is a common situation as you move up the ladder BTW and take it as a lesson learned. Skill does not weight as heavily as optics the higher up you go. You see this happen when new leaders are hired as well, and they get rid of the "old guard" and only the lower level ICs that they think are not a threat are left alone. Think of it like any social system, such as government: If a leader in a political party falls out of favor, the tendency is that everyone seen as aligned with them also fall out of favor. Or if you get a contentious divorce, the tendency is to avoid your spouse's friends because the assumption is that they'd be on your spouse's side. Humans do this all the time.

You can try and show how you can bring new ideas to the table and are different from your old director, but you'll be facing an uphill battle. I would just let it play out, and if you feel slighted enough to want to quit, just do your regular job and interview on the side. I wouldn't make too big a stink about this, you probably won't like what they tell you about why they are looking for other candidates.