Some people feel like they want to stay out of the way and let the new person do things their own way. They don't want to be perceived as trying to continue to manage or run things from afar.

Other people feel like they want to pass on as much info as the new person wants - answer questions, share thoughts, etc., and then let the new person do their thing.

And some people actually do have some thoughts as to where they think the new person should go in the role - and they'll tell them that. In some ways seeming like they want to continue controlling things or setting the agenda for the future.

I've seen all three approaches in various work roles, but also in various church calling roles as well. I'm not sure there is a "best" way - though I would think that trying to set the agenda for the future is out of bounds.