Narcissist come again to party (9)
I believe the answer is:
egomaniac
'narcissist' is the definition.
(I've seen this in another clue)
'come again to party' is the wordplay.
'to party' indicates an anagram (I've seen 'parties' mean this (the letters move or party around)).
'come'+'again'='comeagain'
'comeagain' anagrammed gives 'EGOMANIAC'.
(Other definitions for egomaniac that I've seen before include "self-obsessed individual" , "Highly self-absorbed person" , "Abnormally egotistical person" , "Come again (anag.)" , "Obsessively self-centred person" .)