Extremely dodgy, unpleasant line of hereditary rulers (7)
I believe the answer is:
dynasty
'line of hereditary rulers' is the definition.
(I've seen this before)
'extremely dodgy unpleasant' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'unpleasant' becomes 'nasty' (nasty can mean unpleasant or horrible).
'dodgy' with its centre removed is 'dy'.
'dy'+'nasty'='DYNASTY'
(Other definitions for dynasty that I've seen before include "Sequence of powerful leaders in the same family" , "House" , "show" , "Line of kings" , "Empire" .)