One whom people don't admit is not a favourite (8)
I believe the answer is:
outsider
'not a favourite' is the definition.
(I've seen this before)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for outsider that I've seen before include "non-member required" , "Not a member of the group" , "One unlikely to win" , "Someone excluded" , "Someone not accepted by society" .)