Met to compose anthem (5)
I believe the answer is:
motet
'anthem' is the definition.
(I've seen this in another clue)
'met to compose' is the wordplay.
'compose' is an anagram indicator.
'met'+'to'='metto'
'metto' with letters rearranged gives 'MOTET'.
(Other definitions for motet that I've seen before include "Piece of sacred music" , "Certain one is morally superior" , "10 [COMPOSITION]" , "Unaccompanied choral composition with sacred lyrics" , "Short sacred choral piece" .)