Terrible conceit -- grew endlessly selfish (10)
I believe the answer is:
egocentric
'selfish' is the definition.
(thesaurus)
'terrible conceit grew endlessly' is the wordplay.
'terrible' is an anagram indicator.
'endlessly' means to remove the last letter.
'conceit'+'grew'='conceitgrew'
'conceitgrew' with its last letter removed is 'conceitgre'.
'conceitgre' with letters rearranged gives 'EGOCENTRIC'.
(Other definitions for egocentric that I've seen before include "Self-seeking" , "Self-interested" , "Self-obsessed" , "Self-centred person with little regard for others" , "Selfish" .)