Upwardly mobile officer overheard hostility (7)
I believe the answer is:
rancour
'hostility' is the definition.
(rancour is a kind of hostility)
'upwardly mobile officer overheard' is the wordplay.
I cannot really understand how this works, but
'officer' could be 'nco' (abbreviation for non-commissioned officer) and 'nco' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for rancour that I've seen before include "Bitterness or resentfulness" , "Spite" , "Animosity" , "Bitter feeling or ill will" , "Deep, bitter hate" .)