Letter in Greek about Queen backing city (7)
I believe the answer is:
chennai
'city' is the definition.
(I have seen 'Indian city' mean 'chennai' so perhaps 'city' could also mean 'chennai')
'letter in greek about queen backing' is the wordplay.
'letter in greek' becomes 'chi'.
'about' means one lot of letters goes inside another.
'queen' becomes 'anne' (I've seen this before).
'backing' is a reversal indicator.
'anne' written backwards gives 'enna'.
'chi' enclosing 'enna' is 'CHENNAI'.
(Other definitions for chennai that I've seen before include "Indian city, formerly called Madras" , "Indian port" , "Current name for Madras" , "Official name for Madras" , "City previously called Madras" .)