The curse of Bibiana the Martyr (8)
I believe the answer is:
anathema
'the curse' is the definition.
(anathema can mean a curse)
'of bibiana the martyr' is the wordplay.
'of' indicates the answer is hidden within the clue.
'ANATHEMA' can be found hidden inside 'bibiana the martyr'.
(Other definitions for anathema that I've seen before include "Object of detestation" , "Formal curse leading to excommunication" , "abhorrent" , "Cursed thing" , "Something one vehemently dislikes" .)