Do we have her inquire with her own department to see if they can help influence this in our favor?
I she has a good relationship with her new chair, I would suggest she begin there. Sometimes a chair or a dean can put in a good word, and sometimes a hiring department will be open to that.
Of course (as happened to us) sometimes a department chair with a position available really hates a dean, so just ignores any polite requests. And sometimes a position like that has been created for someone they already have, of course--but it's definitely worth giving it your best shot!