As a new business leader/executive, I would often make management or leadership transitions be a gradual process over several months.
It always turned out badly.
I'd bring on a new person expected to take charge in the some way in the company. Then have them "hang around" for awhile getting "up to speed" before making a real transition.
Now, I recommend making leadership changes immediate and full.
These gradual transitions are tough on the incoming leader. This person has ~90 days to start well with the company. Yet, they're being asked to accomplish that in an ambiguous role? Not gonna happen.
Rapid is better for employees. While you may believe you're helping your employees "get accustomed" to this new person, it's actually confusing for them. Remember that high-performing team members have a clear role including who is their boss.
Gradual management transitions are usually a sign of indecisive leadership. And that type of management is a habit any organization should break.