The costliest takeover mistake happens before any new team arrives. Someone cancels a hosting plan, a domain lapses, or a former supplier's account is shut, and a part of the live system that depended on it stops without warning. Running software often relies on services and credentials you can't see from the main code repository.
The signs that a takeover is due are usually familiar. Nobody is confident enough to release a change. Small bugs collect because fixing one breaks another. A renewal email arrives for a service nobody recognises, and the person who would know has stopped replying.
So the first job is to understand what you have. Keep everything running as it is while we build an inventory and go through it with you.
Change credentials and close accounts after the handover, not before.