Dealing with consumption, try not finishing initially (8)
I believe the answer is:
treating
'dealing with' is the definition.
('treat' can be a synonym of 'deal with')
'consumption try not finishing initially' is the wordplay.
'consumption' becomes 'eating' (eating is a kind of consumption**).
'not finishing' means to remove the last letter.
'initially' is a charade indicator (letters next to each other).
'try' with its last letter taken off is 'tr'.
'eating' put after 'tr' is 'TREATING'.
(Other definitions for treating that I've seen before include "Giving medical attention or paying for someone" , "Negotiating (with); handling" , "Giving medical care to" , "Making no charge" , "Dealing with" .)