Change of heart in right-wing city of old (4)
I believe the answer is:
troy
'city of old' is the definition.
(ancient city)
'change of heart in right-wing' is the wordplay.
'change of heart in' becomes 'tr' (I can't explain this - if you can you should give a lot more credence to this answer).
'right' becomes 'okay' (I've seen this before).
'wing' means to remove the middle letters (I've seen 'wings' mean this (the wings or edge letters of the word are used)).
'okay' with its centre removed is 'oy'.
'tr'+'oy'='TROY'
(Other definitions for troy that I've seen before include "Ancient city, Ilium" , "Ancient city where fair Helen was a captive" , "Ancient beseiged city" , "Ancient city associated with a wooden horse" , "Iliad siege city" .)