Story of prodigious brat produced in America repeatedly (7)
I believe the answer is:
amadeus
'story of prodigious brat' is the definition.
The definition suggests a singular noun which matches the answer.
'produced in america repeatedly' is the wordplay.
'america repeatedly' can mean two replacements for 'america'.
'produced' becomes 'made' ('make' can be a synonym of 'produce').
'in' is an insertion indicator.
'america' becomes 'a' (common abbreviation - e.g. in organisation names).
'america' becomes 'US' (United States).
'a'+'us'='aus'
'made' put inside 'aus' is 'AMADEUS'.
Can you help me to learn more?
(Other definitions for amadeus that I've seen before include "Wolfgang -- Mozart" , "Mozart play/film" , "Mozart's second name" , "Play about Mozart (Shaffer)" , "Quartet" .)