Get a half of bitter that's only a quarter! (6)
I believe the answer is:
winter
'a quarter' is the definition.
(quarter of the year)
'get a half of bitter' is the wordplay.
'get' becomes 'win' (winning is a kind of getting).
'a half of' means to take half the letters.
'bitter' cut in half is 'ter'.
'win'+'ter'='WINTER'
'that's only' acts as a link.
(Other definitions for winter that I've seen before include "period of discontent?" , "Cold period" , "'Now is the . . . . . . of our discontent' (Richard III)" , "'If . . . . . . comes, can spring be far behind?'" , "Cold season" .)