Self-centred person, for example, first is after love (6)
I believe the answer is:
egoist
'self-centred person' is the definition.
(I've seen this before)
'example first is after love' is the wordplay.
'example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'first' becomes 'ist' (ist resembles 1st).
'is after' says to put letters next to each other.
'love' becomes 'o' (love means zero in tennis).
'ist' put after 'o' is 'oist'.
'eg'+'oist'='EGOIST'
'for' is the link.
(Other definitions for egoist that I've seen before include "Selfish type" , "no one should ignore me" , "Conceited person with little regard for others" , "Narcissist" , "A self-interested conceited person" .)