It takes the entire time you know someone to build trust, and only a second to destroy it. As a leader, your team will trust you only as long as they believe that you are a person of integrity. That you will do the right thing no matter the situation. That is how you build trust with your team.
In The Hard Thing About Hard Things, Ben Horowitz recalls a restructuring he initiated so his core company could survive. The bottom line: 150 employees would become employees of another company. And 140 employees would be looking for a job. Instead of going to New York for the announcement, a mentor advised him to go tell his employees where they stood. It could not wait a day.
By showing integrity with these employees, he maintained his trust with the employees who would stay. How have you shown integrity with your team?