for women leaders

Read Fierce Conversations and
Fierce Leadership. Both are excellent. They are also not for everyone; not
everyone can pull off some of the things she recommends. But I still
encourage everyone to read them.
I have been in your situation, more than once. I've both succeeded and
failed at it. The first thing I recommend is DON'T think you can gain their
trust when you walk in the door. It's impossible. Trust needs to be earned.
It's actually something that I talk about when taking on a new team - that
we're new to each other and we're going to have to get to know each other
and that I want to earn their trust. I talk about the things I expect from
them. I ask what they expect from me. I set up individual and team meetings.
I take people to lunch. I try really, really hard not to jump to conclusions
and take some time to hear from everyone. And I try not to let what has
happened previously affect me. Everyone has a clean slate (tell them that)
it's good and it's also bad, because I don't know how well they were
performing previously and we'll need to demonstrate to each other what we're
good at. Always back them up in public, even if they're wrong, so they know
you've got their backs (talk to them about the issue in private and see if
you can help the person fix it himself quietly).
Good luck with the new job! I'm sure you're going to be great.