Right admitted to bias in education (8)
I believe the answer is:
learning
'education' is the definition.
(I know that learning is a type of education)
'right admitted to bias' is the wordplay.
'right' becomes 'r' (common abbreviation).
'admitted to' is an insertion indicator.
'bias' becomes 'leaning' (leaning can mean a bias or tendency).
'r' inserted inside 'leaning' is 'LEARNING'.
'in' acts as a link.
(Other definitions for learning that I've seen before include "(Knowledge from) study" , "Aquiring skill or knowledge" , "Lore" , "Instruction" , "Cognitive process of acquiring skill or knowledge" .)