Not leave time to visit state (4)
I believe the answer is:
stay
'not leave' is the definition.
'time to visit state' is the wordplay.
'time' becomes 't'.
'to visit' is an insertion indicator.
'state' becomes 'say' (say is a kind of state**).
't' put into 'say' is 'STAY'.
(Other definitions for stay that I've seen before include "Supporting rope; remain" , "Stanchion" , "Period in one place" , "Postpone" , "Guy rope" .)