Distrust is a feeling of doubt about some person or thing. We distrust people who aren't honest.
When you trust someone, you believe in her, so the opposite is true of distrust. Trust is from the Old Norse word traust meaning "confidence." Put a dis in front of it, and to distrust is to have no confidence in someone or something. As a noun, distrust is the feeling of doubt. In a corrupt workplace, there will be a lot of distrust. Where there's distrust, there's not much harmony.