An inclination to show prejudice (4)
I believe the answer is:
bias
This clue is a double definition.
'an inclination' is the first definition.
(bias is a kind of inclination)
'prejudice' is the second definition.
('bias' can be a synonym of 'prejudice')
'to show' acts as a link.
(Other definitions for bias that I've seen before include "One-sided inclination" , "One-sided prejudice" , "could be binding" , "Prejudice, one-sidedness" , "Prejudice, partiality" .)