Organ recital, almost exquisite, starts up (3)
I believe the answer is:
ear
'organ' is the definition.
(the ear is an organ)
'recital almost exquisite starts up' is the wordplay.
'starts' suggests taking the first letters.
'up' is a reversal indicator (in down clue: letters go upwards).
The first letters of 'recital almost exquisite' is 'rae'.
'rae' written backwards gives 'EAR'.
(Other definitions for ear that I've seen before include "Listening organ" , "Seed-bearing part of wheat" , "Part of cereal plant containing seed" , "That makes sense" , "'Give every man thine ..., but few thy voice'/Hamlet" .)