1. get yourself familiar with the products (if necessary, take some of your spare time to do it). This is critical because if you don't know enough about the product, people (especially developers) don't even both to talk to you.
2. find out the emphasis of your ex-director, understand what tasks can be handled by lower level managers and QA engineers and what must be handled by the director. Sometimes the director also need to know certain important technical details. Try to get support from your ex-director as much as possible, her comments/advices will be extremely valuable to you.
3. if possible, call for a meeting with your people, understand their task assignments and their opinions, existing issues. Usually QA engineers/managers have certain relation with dev people, encourage them to keep communication with dev people. If you can make your people keep doing good job (e.g. file a bunch of priority 0 bugs :) ), dev people will respect you slowly.
4. build up your own work relationship with dev people. More communication with them to set their expections right. And if possible get support from your boss.
Trust cannot be built up over the night, but you need to convey the information to dev people that you and your team are on the right track.
Just my 1cent.:) Good luck.