Wary bishop is hosting Democrat Eddy near Sicily (9)
I believe the answer is:
charybdis
'eddy near sicily' is the definition.
(whirlpool sea monster in Greek myth)
'wary bishop is hosting democrat' is the wordplay.
'wary' becomes 'chary' ('chary' can be a synonym of 'wary'**).
'bishop' becomes 'b' (abbreviation used in chess).
'hosting' indicates putting letters inside.
'democrat' becomes 'd'.
'b'+'is'='bis'
'bis' enclosing 'd' is 'bdis'.
'chary'+'bdis'='CHARYBDIS'
(Other definitions for charybdis that I've seen before include "Scylla's counterpart" , "monster" , "Whirlpool opposite Scylla" , "Whirlpool, across from 14" , "Mythical whirlpool" .)