Thus old city becomes bitter (4)
I believe the answer is:
sour
'bitter' is the definition.
(I've seen this before)
'thus old city' is the wordplay.
'thus' becomes 'so' (synonyms).
'old city' becomes 'ur' (ancient city state).
'so'+'ur'='SOUR'
'becomes' acts as a link.
(Other definitions for sour that I've seen before include "Curdled" , "Acid - bitter" , "Turned - morose" , "Bitter, tart" , "Acid, tart" .)