I would say have compassion and flexibility, but don't let people walk all over you. Don't be afraid to ask for what you need, like 5 minutes to finish a task before addressing their issue. If people are complaining, I will often ask them to come up with a solution. I definitely agree that stepping into a leadership position internally is more difficult than starting as a leader in a new facility. One of the most helpful things that I was told early in my career was to vent up, personnel management can be frustrating, but go vent to a supervisor or manager away from the lab, this can often help bring perspective to the situation.
Good luck!