Powerful family, extremely dirty and disgusting (7)
I believe the answer is:
dynasty
'powerful family' is the definition.
(I've seen this before)
'extremely dirty and disgusting' is the wordplay.
'extremely' suggests removing the centre (letters on the extremes of the word are used).
'and' is a charade indicator (letters next to each other).
'disgusting' becomes 'nasty' (I've seen this before).
'dirty' with its centre taken out is 'dy'.
'dy'+'nasty'='DYNASTY'
(Other definitions for dynasty that I've seen before include "Powerful family line" , "House" , "show" , "Family line of rulers" , "royal family" .)