Turn down short side road (4)
I believe the answer is:
spur
'side road' is the definition.
(I've seen this before)
'turn down short' is the wordplay.
'turn down' becomes 'spurn' ('spurn' can be a synonym of 'turn down').
'short' means to remove the last letter.
'spurn' with its final letter taken away is 'SPUR'.
(Other definitions for spur that I've seen before include "slip road" , "side road" , "Sharp pointed projection" , "Encourage" , "Goad, prod" .)