Almost nobody has time (4)
I believe the answer is:
noon
'time' is the definition.
(noon is a kind of time)
'almost nobody' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'nobody' becomes 'no one' (not a single person).
'noone' with its last letter taken away is 'NOON'.
'has' acts as a link.
(Other definitions for noon that I've seen before include "when PM starts" , "Twelve o'clock in the day" , "12 pm" , "A moment of time" , "See 8" .)