Attempt with publicity to provoke (4)
I believe the answer is:
goad
'provoke' is the definition.
(goading is a kind of provoking)
'attempt with publicity' is the wordplay.
'attempt' becomes 'go' (go is a kind of attempt).
'with' says to put letters next to each other.
'publicity' becomes 'ad' (advert).
'go'+'ad'='GOAD'
'to' is the link.
(Other definitions for goad that I've seen before include "Provoke, spur" , "Prod with a pointed stick" , "Incentive" , "Incite to action" , "Cattle-driving spike" .)