Composer’s astonishing feat, in captivating monarch (8)
I believe the answer is:
couperin
'composer's' is the definition.
(Francois Couperin)
'astonishing feat in captivating monarch' is the wordplay.
'astonishing feat' becomes 'coup' (coup can mean an impressive feat or achievement).
'captivating' means one lot of letters goes inside another (I've seen this in other clues).
'monarch' becomes 'ER' (abbreviation for Elizabeth Regina, British Queen).
'coup'+'in'='coupin'
'coupin' enclosing 'er' is 'COUPERIN'.
(Other definitions for couperin that I've seen before include "Francois -, seventeenth-eighteenth century French composer" , "he made notes" , "Franois -, French rococo composer" .)