Briefly turn down side road (4)
I believe the answer is:
spur
'side road' is the definition.
(I've seen this before)
'briefly turn down' is the wordplay.
'briefly' means to remove the last letter.
'turn down' becomes 'spurn' (synonyms).
'spurn' with its last letter taken away is 'SPUR'.
(Other definitions for spur that I've seen before include "branch road" , "Incentive; branch line" , "Goad - branch line" , "Strong incentive" , "Provoke" .)