It takes time
You cannot avoid suspicion from your team when you first join or when they join your team. You & a new IC will be strangers at first and as any other relationship it has to be built and it takes time. When you join a team you are the odd one in a somewhat functioning system. When someone joins your team the whole environment will be new for them and they will look to understand if they can believe you and that you are not going to screw them over, after all they have to go through the probation period.
Communication
Communication is the most important in building trust. Everything you say can be interpreted differently depending on the level of trust they have and it will be received with a different level of skepticism. Honesty is always best, but there is no need for 100% transparency and as a manager you’ll be withholding information from your team from time to time. Omitting isn’t lying. After all, a good manager is a good shit shield for their team and a bad one will be a shit funeller.
Trust
A negative scenario in the team can become a rallying point for a team. Trust is the foundation for a healthy & long collaboration.
Tone
Your direct reports will always eventually match your own behavior, thus it’s important to pay attention to your non verbal communication. Thus it’s important to display what you seem appropriate to the situation: seriousness, light-weightness etc. A good example is during an incident, you have to be serious and set the tone, otherwise you won’t give the message that it is something that is severe.