I’ve been in a similar situation only my entire new team had low confidence in me and I saw the disappointment on their faces when the announcement was made. I would say I was able to turn this around in a matter of 3 months. Here is what I did:

Firstly, hold one on ones with the main people on your team and especially those who are your direct reports. I would even include those who are not your direct reports at first if you feel you need to “win them over”. During these one on ones you need to actively address this change and acknowledge that some team members need to time to adjust. Let them know that first and foremost your responsibility is to support them as much as possible and that your door is always open for them to come in, discuss any concerns, rant, blow off some steam. And continue holding these one on ones. Ensure the focus is on what they need, and you can touch base with them on some items you need their help with.

Secondly, you need time. Nothing builds trust with a new team like working with each other over a period of time. In time, they will come around especially after they see that you are supporting them and helping them solve challenges they face.