Contemptuously reject what's new after incitement (5)
I believe the answer is:
spurn
'contemptuously reject' is the definition.
(I've seen this before)
'new after incitement' is the wordplay.
'new' becomes 'n'.
'after' says to put letters next to each other.
'incitement' becomes 'spur' (spur is a kind of incitement).
'n' after 'spur' is 'SPURN'.
'what's' acts as a link.
(Other definitions for spurn that I've seen before include "Reject advances scornfully" , "Repulse" , "Reject scornfully, say unwanted suitor" , "Show contempt for" , "Reject with contempt" .)