Private Society avoided admitting Conservative (8)
I believe the answer is:
secluded
'private' is the definition.
(similar in meaning)
'society avoided admitting conservative' is the wordplay.
'society' becomes 's' (common abbreviation in names of organisations).
'avoided' becomes 'eluded' (eluding is a kind of avoiding).
'admitting' means one lot of letters goes inside another (admit can mean to welcome in or accept).
'conservative' becomes 'C' (UK political abbreviation).
'eluded' going around 'c' is 'ecluded'.
's'+'ecluded'='SECLUDED'
(Other definitions for secluded that I've seen before include "Out of sight - away from society" , "Sheltered and private" , "Private - withdrawn" , "Out of the way" , "Out-of-the-way" .)