Bitter writer follows cycling race (7)
I believe the answer is:
acerbic
'bitter' is the definition.
(synonyms)
'writer follows cycling race' is the wordplay.
'writer' becomes 'bic' (kind of pen).
'follows' is a charade indicator (letters next to each other).
'cycling' is an anagram indicator.
'race' is an anagram of 'acer'.
'bic' after 'acer' is 'ACERBIC'.
(Other definitions for acerbic that I've seen before include "Sour; sharp" , "Harsh and sharp in speech" , "Sharp, forthright" , "Astringent; sour" , "Biting" .)