Refuse with contempt, lacking new incentive (4)
I believe the answer is:
spur
'incentive' is the definition.
(thesaurus)
'refuse with contempt lacking new' is the wordplay.
'refuse with contempt' becomes 'spurn' (I've seen this before).
'lacking' is a deletion indicator.
'new' becomes 'n'.
'spurn' with 'n' removed is 'SPUR'.
(Other definitions for spur that I've seen before include "Stimulate" , "Cowboy's goading instrument" , "Goad; stimulus" , "'Urge, goad (4)'" , "Goad - incentive" .)