A four letter word for 'don't go' is stay.
COME...come! dont go, come!
fire
goalgoatgodsgoesgoldgolfgonegonggoodgoongown
pass
rise
seek
Gone
COME
here
seek
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