Produce army officer's short note (8)
I believe the answer is:
generate
'produce' is the definition.
(I know that generate is a type of produce)
'army officer's short note' is the wordplay.
'army officer' becomes 'general' (type of army officer).
'short' means to remove the last letter.
'note' becomes 'te' (musical note).
'general' with its last letter removed is 'genera'.
'genera'+'te'='GENERATE'
(Other definitions for generate that I've seen before include "Bring into existence for teenager" , "Create (power)" , "Produce, electricity say" , "evolve" , "Beget" .)