Self-centred person? Eccentric? Come again? (9)
I believe the answer is:
egomaniac
'self-centred person?' is the definition.
The answer and definition can be both people as well as being singular nouns.
Maybe you can see an association between them that I can't see?
'eccentric? come again?' is the wordplay.
'eccentric?' indicates anagramming the letters (I've seen 'eccentric' mean this).
'come'+'again'='comeagain'
'comeagain' anagrammed gives 'EGOMANIAC'.
Can you help me to learn more?
(Other definitions for egomaniac that I've seen before include "Highly self-absorbed person" , "Obsessively self-centred person" , "he thinks "it's all about ME"" , "Come again (anag.)" , "One who's self-obsessed" .)