To gripe about act of self-aggrandisement (3,4)
I believe the answer is:
ego trip
'act of self-aggrandisement' is the definition.
(I've seen this before)
'to gripe about' is the wordplay.
'about' indicates anagramming the letters.
'to'+'gripe'='togripe'
'togripe' anagrammed gives 'EGO TRIP'.
(Other definitions for ego trip that I've seen before include "Exercise in self-indulgence" , "Self-boosting activity" , "morale-boosting experience" , "Act of self-aggrandisement" , "Activity boosting one's self-importance" .)