New senior leaders are watched closely. In the first few weeks, every meeting, question and decision is read as a signal of what kind of leader you will be. Used well, the first ninety days build trust that lasts for years.
Meet people at every level, not only your direct reports. Ask three questions: what is working, what is getting in the way, and what would you change if you were in my seat. Write down what you hear and look for patterns.
Pick two or three problems that matter to the people you lead and that you can genuinely solve quickly. Visible progress on a long-standing frustration earns more trust than a grand announcement.
By now you know enough to share your priorities. Explain them with what you learned from listening, so people recognise their own input. Make the team decisions you have been considering, fairly and clearly.
A coach or trusted peer can help you test your thinking during this period. The aim is not to have every answer, but to show that you are listening, learning and willing to decide.