Hear about the Italian bishop's hat (6)
I believe the answer is:
trilby
'hat' is the definition.
(trilby is a kind of hat)
'hear about the italian bishop's' is the wordplay.
'hear' becomes 'try' ('try' can be a synonym of 'hear').
'about' indicates putting letters inside.
'the italian' becomes 'il' (the in Italian).
'bishop' becomes 'b' (abbreviation used in chess).
'il'+'b'='ilb'
'try' placed around 'ilb' is 'TRILBY'.
(Other definitions for trilby that I've seen before include "Type of hat" , "Felt hat with a creased crown" , "kind of headgear" , "Style of hat" , "Book by George du Maurier - hat" .)