One primarily relishing beer — bitter (5)
I believe the answer is:
acerb
'bitter' is the definition.
(synonyms)
'one primarily relishing beer' is the wordplay.
'one' becomes 'ace' (ace has a value of one in some card games).
'primarily' says to take the initial letters.
The initial letters of 'relishing beer' is 'rb'.
'ace'+'rb'='ACERB'
(Other definitions for acerb that I've seen before include "sharp" , "harsh and bitter" , "tart" , "Sour, bitter" .)