Reject, lacking new incentive (4)
I believe the answer is:
spur
'new incentive' is the definition.
'spur' can be an answer for 'incentive' (I've seen this before). I am not certain of the 'new' bit.
'reject lacking' is the wordplay.
'reject' becomes 'spurn' (synonyms).
'lacking' means to remove the last letter (the word is incomplete or lacking).
'spurn' with its final letter taken off is 'SPUR'.
Can you help me to learn more?
(Other definitions for spur that I've seen before include "Goad as for use by horse-rider" , "Inducement" , "Strong incentive" , "Cowboy's goading instrument" , "Projection on cock's leg" .)