[win] {one's} trust

to earn the confidence, belief, or reliance of another person

It took time and honesty to win her trust after a period of misunderstandings.
The candidate's consistent actions and transparency helped him win the voters' trust.
Building a strong track record of reliability is crucial to winning customers' trust.
In a relationship, open communication and mutual respect are essential to winning each other's trust.
The dedicated nurse's compassionate care helped her win the patient's trust.