Very big self-obsession, Georgia (4)
I believe the answer is:
mega
'very big' is the definition.
(I've seen this before)
'self-obsession georgia' is the wordplay.
'self-obsession' becomes 'me' (as in 'me me me').
'georgia' becomes 'ga'.
'me'+'ga'='MEGA'
(Other definitions for mega that I've seen before include "extremely good" , "Game (anag) - excellent" , "Huge (slang)" , "Fantastic!" , "Very large (colloq.)" .)