Female holding up opening part of choral piece (7)
I believe the answer is:
strophe
'choral piece' is the definition.
(a strophe is part of a Greek ode)
'female holding up opening part' is the wordplay.
'female' becomes 'she' (I've seen this before).
'holding' means one lot of letters goes inside another.
'up' is a reversal indicator (in down clue: letters go upwards).
'opening part' becomes 'port' (eg a computer port).
'port' in reverse letter order is 'trop'.
'she' going around 'trop' is 'STROPHE'.
'of' is the link.
(Other definitions for strophe that I've seen before include "Part of a lyric poem" , "song for chorus" , "Section of lyric poem" , "Division of choral ode" , "stanza" .)