Self-centred person, say, gets nothing first (6)
I believe the answer is:
egoist
'self-centred person' is the definition.
(I've seen this before)
'say gets nothing first' is the wordplay.
'say' becomes 'eg'.
'gets' says to put letters next to each other.
'nothing' becomes 'O' (looks like zero - 0).
'first' becomes 'ist' (ist resembles 1st).
'eg'+'o'+'ist'='EGOIST'
(Other definitions for egoist that I've seen before include "He puts himself first" , "Conceited and self-centred person" , "Bighead" , "Conceited person with little regard for others" , "A seld-centred, conceited person" .)