You must be in a position to produce what you promise. Failure to do so causes people to lose faith in your competence. They, therefore, don't trust that you can provide what you say. Being clear about what you can and cannot do and paying attention to the details when delivering will demonstrate that you are trustworthy. The second imperative of building trust is a combination of honesty and consistency.
Employees trust supervisors who are honest in what they say and consistent in how they act.
Behaving with integrity starts by defining clear purpose and articulating what is expected. Once the expectations are known, acting with integrity requires having the strength to deal with reality. Problems or negative information can never be hidden or sugar coated. Integrity requires that all information be open. The third imperative of building trust, showing concern for others, is also necessary to demonstrate the importance of the supervisor-employee relationship.