Fine organic compound's gradually become bitter (6)
I believe the answer is:
fester
'gradually become bitter' is the definition.
(fester can mean to gradually become rotten)
'fine organic compound's' is the wordplay.
'fine' becomes 'f' (abbreviation).
'organic compound' becomes 'ester' (ester is a kind of organic compound).
'f'+'ester'='FESTER'
(Other definitions for fester that I've seen before include "Become rotten, bitter or irritated" , "Ripen and generate pus" , "strange uncle" , "Of wound, become septic and filled with pus" , "Putrefy" .)