Socialist prejudice all but admitted by enthusiast (6)
I believe the answer is:
fabian
'socialist' is the definition.
(Fabian is an example)
'prejudice all but admitted by enthusiast' is the wordplay.
'prejudice' becomes 'bias' ('bias' can be a synonym of 'prejudice').
'all but' means to remove the last letter ('all but' can mean 'almost' or 'nearly').
'admitted by' means one lot of letters goes inside another.
'enthusiast' becomes 'fan' (fan is a kind of enthusiast).
'bias' with its last letter taken away is 'bia'.
'bia' going within 'fan' is 'FABIAN'.
(Other definitions for fabian that I've seen before include "who belongs to a left-wing society" , "one joining 10 27 21 [INDEPENDENT LABOUR PARTY] ?" , "British socialist" , "[SLEUTH]" , "cautious" .)