Private person who’s offended possibly rejecting society (5)
I believe the answer is:
inner
'private' is the definition.
(as in one's private or inner thoughts)
'person who's offended possibly rejecting society' is the wordplay.
'person who's offended possibly' becomes 'sinner' (someone who has offended).
'rejecting' indicates named letters should be taken away.
'society' becomes 's' (common abbreviation in names of organisations).
'sinner' with 's' taken away is 'INNER'.
(Other definitions for inner that I've seen before include "Inside; next to the bull (archery)" , "Exclusive to a center" , "Interior" , "(Hit on) part of target immediately next to the bullseye" , "Internal - mental" .)