Jibing at heart when showing prejudice (4)
I believe the answer is:
bias
'prejudice' is the definition.
(I know that prejudice can be written as bias)
'jibing at heart when' is the wordplay.
'at heart' means to look at the middle letters.
'when' becomes 'as' (eg 'when I walked' means 'as I walked').
The middle letters of 'jibing' are 'bi'.
'bi'+'as'='BIAS'
'showing' is the link.
(Other definitions for bias that I've seen before include "colour" , "Inclination of prejudice" , "Favouritism" , "Unfairly influence" , "One-sided inclination" .)