Female soldier beginning to organise slow movement (6)
I believe the answer is:
adagio
'slow movement' is the definition.
(slow musical movement)
'female soldier beginning to organise' is the wordplay.
'female' becomes 'Ada' (woman's name).
'soldier' becomes 'GI' (term for US soldier).
'beginning to' suggests taking the first letters.
The initial letter of 'organise' is 'o'.
'ada'+'gi'+'o'='ADAGIO'
(Other definitions for adagio that I've seen before include "Slow movement (music)" , "In slow time (music)" , "In slow time (mus.)" , "moving slowly" , "Slowly, from a conductor" .)