Publicity man wildly resents gap (5,5)
I believe the answer is:
press agent
'publicity man' is the definition.
(synonyms)
'wildly resents gap' is the wordplay.
'wildly' is an anagram indicator.
'resents'+'gap'='resentsgap'
'resentsgap' is an anagram of 'PRESS-AGENT'.
(Other definitions for press agent that I've seen before include "PR person" , "PA" , "Person seeking favourable publicity on behalf a client" , "publicist" .)