Incitement to gush endlessly (4)
I believe the answer is:
spur
'incitement' is the definition.
(spur is a kind of incitement)
'gush endlessly' is the wordplay.
'gush' becomes 'spurt' ('spurt' can be a synonym of 'gush').
'endlessly' means to remove the last letter.
'spurt' with its last letter taken away is 'SPUR'.
'to' is the link.
(Other definitions for spur that I've seen before include "Impel" , "Goad - incentive" , "Device to urge on a horse" , "Prompt" , "Incentive; branch line" .)