Don't be oblivious about one in society (8)
I believe the answer is:
remember
'don't be oblivious' is the definition.
I can't tell whether this definition defines the answer.
'about one in society' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'one in society' becomes 'member' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
're'+'member'='REMEMBER'
Can you help me to learn more?
(Other definitions for remember that I've seen before include "Bring the past to mind" , "Commemorate" , "Think back" , "Recall to mind" , "Bear in mind" .)