Concern for oneself, say: nothing is mentioned at first (6)
I believe the answer is:
egoism
'concern for oneself' is the definition.
(egoism is obsession with one's self)
'say nothing is mentioned at first' is the wordplay.
'say' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'nothing' becomes 'O' (looks like zero - 0).
'at first' says to take the initial letters.
The first letter of 'mentioned' is 'm'.
'eg'+'o'+'is'+'m'='EGOISM'
(Other definitions for egoism that I've seen before include "Self-centredness, conceit" , "Self-centredness, vanity" , "principle of self-interest" , "Self-seeking" , "sense of superiority" .)