A four letter word for 'don't go' is stay.
COME...come! dont go, come!
goalgoatgodsgoesgoldgolfgonegonggoodgoongown
fire
pass
COME
seek
here
rise
seek
Gone
You may be going for the word flit.
There is more than one 4-letter word that means "to go in search of."To go in search of:S for seekH for huntL for look