Again, come out for self-styled VIP (9)
I believe the answer is:
egomaniac
'self-styled vip' is the definition.
'again come out' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'again'+'come'='againcome'
'againcome' is an anagram of 'EGOMANIAC'.
'for' acts as a link.
(Other definitions for egomaniac that I've seen before include "Self-obsessed person" , "he thinks "it's all about ME"" , "Obsessively self-absorbed person" , "who's full of himself" , "Bighead" .)