Every time I have been taken a new assignment in a new organization, the first question that was asked of me was “What are you going to do first?” My answer was invariably the same one. I would reply “I am first going to learn”. I would give this answer to both the people I reported to, as well as the people that reported to me.
It is good to come into a new role with a rough idea about what may or may not need to be done. This helps you create the first action plan. What normally happens then is that both your preconceived ideas and your plan rarely survive the first encounter with the actual business realities of the assignment intact. It is then that you learn why the situation is in the state it is in.
Machiavelli noted that the two principle ways to govern a new organization were to either go live amidst the existing leadership structure, or to destroy the existing structure and replace it with your own. I have been in corporate cultures where both approaches have been the norm. The team replacement culture usually breeds a business culture of fear, whereas the more inclusive approach will create a more constructive environment for the business.
I have found that my personal preference is to go and locate amidst the existing structure. In this way you can facilitate and speed up your learning process regarding the business. The existing team will always have some stake hold in the existing structures and processes of the business, but in general they will also know that a leadership change has been made for a reason. That reason is to usually change the direction of the business. This is usually easier to do with a team that is familiar with you instead of one that is afraid.