Prayer an hour after midnight inspiring music, initially (4)
I believe the answer is:
imam
'prayer' is the definition.
(leader of Islamic prayer - someone who prays)
'an hour after midnight inspiring music initially' is the wordplay.
'an hour after midnight' becomes 'iam' (1am).
'inspiring' means one lot of letters goes inside another.
'initially' suggests taking the first letters.
The initial letter of 'music' is 'm'.
'iam' placed around 'm' is 'IMAM'.
(Other definitions for imam that I've seen before include "Muslim holy man" , "Ma, I'm off to find religious Muslim" , "Islamic prayer leader" , "Islamic minister" , "Accompaniment in baroque music" .)