You start a new contract as the outsider, and everybody (who doesn’t already know you) treats you with suspicion. My plan for a new contract is always to produce something tangible in the first week. It could be a neat way to solve a problem, a simple explanation to a problem experienced by several colleagues, or a new report/data set/macro.
After that you may be asked for your advice, and you should work hard to give it as simply as possible. Then you get asked more questions, which develop into trust. It never happens overnight, but a freelance contractor is a resource to be valued and used!