And that office goes unfilled during that term. No recess appointments, or temporary fill-ins. No deputy holding down the fort. Just nothing.
But, but but what about the new laws?
Can you imagine if POTUS went unfilled for 4 years?
There'd need to be a CinC contingency fill-in for defense purposes, where the previous SecDef or the current Speaker of the House acts as CinC in the event of a war, but otherwise no new legislation can be passed as there is no POTUS.