Bitterness of promoted soldier, we hear (7)
I believe the answer is:
rancour
'bitterness' is the definition.
(I know that bitterness can be written as rancour)
'promoted soldier we hear' is the wordplay.
'promoted soldier' becomes 'ranker' (soldier promoted up from the ranks).
'we hear' indicates a 'sounds like' (homophone) clue.
'ranker' sounds like 'RANCOUR'.
'of' is the link.
(Other definitions for rancour that I've seen before include "Deep, bitter hate" , "Hard feelings" , "generating ill-feeling ..." , "Long-lasting bitterness" , "Bitter feeling or ill-will" .)