Case of dirty, filthy family (7)
I believe the answer is:
dynasty
'family' is the definition.
(I know that dynasty is a type of family)
'case of dirty filthy' is the wordplay.
'case of' suggests removing the centre (like emptying a case).
'filthy' becomes 'nasty' (synonyms).
'dirty' 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" , "Line of kings" , "Succession of rulers from one family" , "Sequence of hereditary rulers" , "royal family" .)