Self-centredness of some GI, strangely enough (6)
I believe the answer is:
egoism
'self-centredness' is the definition.
(I've seen this before)
'some gi strangely enough' is the wordplay.
'strangely enough' indicates anagramming the letters.
'some'+'gi'='somegi'
'somegi' with letters rearranged gives 'EGOISM'.
'of' acts as a link.
(Other definitions for egoism that I've seen before include "Self interest" , "sense of superiority" , "Exaggerated sense of one's own importance" , "self-centred doctrine" , "principle of self-interest" .)