Delegation [to whom, and how much] is, I think, a very big decision early in a new job at a higher level. It usually becomes necessary before you are fully up and running, as the personal "must do" list starts to get too long.
In a big organisation it helps enormously if you have met some of your new staff in a previous post. Some to trust, some to watch.
I rather think that I got lucky more than once, with some excellent deputies. And I spotted the sh1t before he did any damage.