Born in hushed capital city (6)
I believe the answer is:
mumbai
'city' is the definition.
(I've seen this before)
'born in hushed capital' is the wordplay.
'born' becomes 'b' (abbreviation next to the year of someone's birth).
'in' indicates putting letters inside.
'hushed' becomes 'mum' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'capital' becomes 'ai' (resembles 'Am', old-fashioned term for excellent).
'mum'+'ai'='mumai'
'b' placed inside 'mumai' is 'MUMBAI'.
Can you help me to learn more?
(Other definitions for mumbai that I've seen before include "It used to be called Bombay" , "place in India" , "Bombay since 1995" , "City once called Bombay" , "Indian city formerly known as 4" .)