A soldier in trouble for slow movement (6)
I believe the answer is:
adagio
'slow movement' is the definition.
(slow musical movement)
'a soldier in trouble' is the wordplay.
'soldier' becomes 'GI' (GI can mean a US soldier).
'in' is an insertion indicator.
'trouble' becomes 'ado' (both can mean bother or commotion).
'a'+'gi'='agi'
'agi' inserted into 'ado' is 'ADAGIO'.
'for' is the link.
(Other definitions for adagio that I've seen before include "Slow musical passage" , "going slowly in work" , "In music, leisurely" , "(A movement) to be played slowly" , "Slowly and gracefully, musically" .)