Bishop, when touring Italy, shows this tendency (4)
I believe the answer is:
bias
'this tendency' is the definition.
(bias is a kind of tendency)
'bishop when touring italy' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'when' becomes 'as' (eg 'when I walked' means 'as I walked').
'touring' means one lot of letters goes inside another (touring can mean going round).
'italy' becomes 'i'.
'b'+'as'='bas'
'bas' placed around 'i' is 'BIAS'.
'shows' acts as a link.
(Other definitions for bias that I've seen before include "Prejudice, partiality" , "A leaning or prejudice" , "Bigotry" , "Prejudice for one side" , "(Bowls) irregular shape" .)