The part farthest from the middle (4)
I believe the answer is:
edge
'the part farthest from the middle' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for edge that I've seen before include "Lip; advantage" , "Outer limit" , "'Border, boundary, rim (4)'" , "Brim" , "Move slowly" .)