Bashful about a couple of bishops? That's contemptible (6)
I believe the answer is:
shabby
'contemptible' is the definition.
(thesaurus)
'bashful about a couple of bishops?' is the wordplay.
'bashful' becomes 'shy' (bashful means shy or reserved).
'about' means one lot of letters goes inside another.
'couple of bishops?' becomes 'BB' (abbreviation for bishop, repeated).
'a'+'bb'='abb'
'shy' placed around 'abb' is 'SHABBY'.
'that's' acts as a link.
(Other definitions for shabby that I've seen before include "'Scruffy, tattered (6)'" , "Worn and run-down, like clothes" , "Badly clad - sort of trick?" , "Unworthy" , "Scruffy; unfair" .)