Leave fairly shortly (4)
I believe the answer is:
quit
'leave' is the definition.
(quitting is a kind of leaving)
'fairly shortly' is the wordplay.
'fairly' becomes 'quite' (I've seen this before).
'shortly' means to remove the last letter.
'quite' with its last letter taken away is 'QUIT'.
(Other definitions for quit that I've seen before include "Give up or abandon a task" , "Leave or abandon" , "Give up (smoking?)" , "Leave or stop doing" , "Depart, resign from" .)