Jon Penn's Answer:
My immediate thought was, “I wonder what sort of coaching culture there is in this company?”
If the new Director is not based there, and is so busy and unavailable, and you have a good personal relationship with the team members, it seems quite natural that they should approach you. But are they approaching you for direction or for help?
Hopefully when you do talk to them it is along the lines of open questions, teasing out from them themselves what the real issues are, what the options are, and how they can get to a good decision on next actions. I would be up front with them that it’s not your place to give direction, but you aren’t refusing to help them reach their own decisions.
You don’t say how recent all these changes are, but I guess pretty recent. You will be familiar with the theories around resistance to change: first shock and denial, then testing the decision by old behaviour, eventually either opting out [in mind or in body] or acceptance and then engagement. Could you be witnessing the “testing the decision” stage?
The “lack of leadership” accusation might also fit with this theory. I hope, since you say in your questions that “the new Director seems very good”, that you are sharing that opinion loud and clear with the people who make these comments. Could you maybe suggest to him, as he isn’t present in the workspace that he might devote some time to a bit of team rapport building to get to know the guys better. Also if he isn’t present, is there a system to schedule one to one time with the team on a regular basis?
It sounds like your job is very collaborative and for you to succeed you need all those interactions, so I definitely do not think you should avoid contact with your peers and former reports - but rather be very clear in how you deal with them by supporting the new director, coaching them to a resolution where appropriate, and telling the new director what you did and giving him the option to pick the issues up with them.