Said another way, we can trust people to do what they have done in the past. Or another way, the best predictor of the future is the past, unless there is some intervention that has made things different. That is a track record.
If the team is going to trust someone, that person is going to have to build a track record of bringing results in some area. Of performing well in that ability. Of delivering well in what has been promised. Or at least having delivered in ways that would logicallymake sense to trust her in this new way.