Self-seeker say starts to obsess, thinking immensely selfish thoughts (7)
I believe the answer is:
egotist
'self-seeker' is the definition.
(thesaurus)
'say starts to obsess thinking immensely selfish thoughts' is the wordplay.
'say' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'starts to' says to take the initial letters.
The first letters of 'obsess thinking immensely selfish thoughts' is 'otist'.
'eg'+'otist'='EGOTIST'
(Other definitions for egotist that I've seen before include "Excessively conceited person" , "One excessively conceited" , "Bighead" , "Self-important person" , "One who talks only of self" .)