Composer raised in Rimini's so rich (7)
I believe the answer is:
rossini
'composer' is the definition.
(Italian composer Gioachino Rossini)
'raised in rimini's so rich' is the wordplay.
'raised' says the letters should be written backwards (going up in a down clue).
'in' indicates a hidden word.
'inissor' can be found hidden inside 'riminis so rich'.
'inissor' back-to-front is 'ROSSINI'.
(Other definitions for rossini that I've seen before include "Staff writer" , "Composer born 29 Feb 1792" , "Great musician" , "Composer of The Thieving Magpie" , "He composed operas" .)