Too many people I know blame their predecessor for what is going wrong now. That immediately leads to a loss of credibility. The moment you step into a job or position, you own it. Others will know what belongs to you and what was left when you arrived. Whatever needs changing, change it. Whatever needs to remain, let it remain.
The best testimony of your leadership and trustworthiness is which direction you take from the first day forward. Let what you do speak louder than what you claim. Thinking people will interpret is correctly, and you have nothing to worry about. The sooner you are seen doing the job, the sooner you create an atmosphere of trust.
This is not necessarily easy, but must be intentional. Actually, it will in time be very satisfying, and you will enjoy the way those you work with develop and grow. They will learn to tackle a new assignment the same way, and will get results. This is the way to extend your influence, and then be able to step aside when the time comes and leave things to others and be content with what you have done. The goal is to leave it better than you found it.