Leave, almost completely (4)
I believe the answer is:
quit
'leave' is the definition.
(quitting is a kind of leaving)
'almost completely' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'completely' becomes 'quite' (I've seen this before).
'quite' with its last letter removed is 'QUIT'.
(Other definitions for quit that I've seen before include "Give up or abandon a task" , "Leave one's post" , "Stop; resign" , "Stop (smoking, perhaps)" , "Desist" .)