"To trust the person" means to have confidence and belief in someone's honesty, reliability, and abilities. It means that you rely on them to do what they say they will do and to be truthful and dependable. Full definition
We don't trust people who don't like dogs, either. (geekwrapped.com)
You can not trust the people who tell you whom to trust. (monbiot.com)
Your needs are important, too — you should trust this person with giving your daughter appropriate information about important decisions in her life. (kidshealth.org)