Hostile team member

So, I've been leading a team of 10 teachers for about a month. I've tried to breathe a little bit of life into the team by unifying them around a few small commitments (like asking them all to commit to teach things consistently and stick to deadlines for assignments being conducted). It's all gone well, except for 'David'. David is about 20 years my senior and has quite a bit more experience in education. David is quite confrontational and hostile towards me, and some of the small changes I've talked about making. David seems to think that the things I do are oppressive, or directed at him. I think he has been allowed so much rope for so long that any accountability looks punitive to him now. At the moment, David is the only real present risk to team unity - but I think the rest of the team don't hang on his every word or even respect him a great deal. So, how do I respond to David...?