Selfish behaviour to gripe about (3,4)
I believe the answer is:
ego trip
'selfish behaviour' is the definition.
(I've seen this before)
'to gripe about' is the wordplay.
'about' indicates an anagram.
'to'+'gripe'='togripe'
'togripe' anagrammed gives 'EGO TRIP'.
(Other definitions for ego trip that I've seen before include "totally selfish" , "Self-centred journey?" , "something to boost self-esteem" , "that involves swelling of head?" , "A self-obsessed outing?" .)