Staff getting on and coping with difficulties (8)
I believe the answer is:
managing
'coping with difficulties' is the definition.
'staff getting on' is the wordplay.
'staff' becomes 'man' (manning is a kind of staffing).
'getting on' becomes 'aging' (I've seen this before).
'man'+'aging'='MANAGING'
'and' is the link.
(Other definitions for managing that I've seen before include "Running; coping" , "Handling" .)