Counts are disturbed by a mistress (9)
I believe the answer is:
courtesan
'a mistress' is the definition.
(I know that mistress can be written as courtesan)
'counts are disturbed' is the wordplay.
'disturbed' is an anagram indicator (the order of letters is disturbed).
'counts'+'are'='countsare'
'countsare' with letters rearranged gives 'COURTESAN'.
'by' is the link.
(Other definitions for courtesan that I've seen before include "paramour" , "odalisque" , "Prostitute - mistress of high-ranking man" , "Kept woman" , "High-class prostitute" .)