Extremely dirty and horrible family (7)
I believe the answer is:
dynasty
'family' is the definition.
(I know that dynasty is a type of family)
'extremely dirty and horrible' is the wordplay.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'and' means one lot of letters go next to another.
'horrible' becomes 'nasty' (I've seen this before).
'dirty' with its centre removed is 'dy'.
'dy'+'nasty'='DYNASTY'
(Other definitions for dynasty that I've seen before include "Family of successive rulers" , "Song perhaps" , "TV series" , "Ruling sequence" , "royal family" .)