House in decay, gutted and filthy (7)
I believe the answer is:
dynasty
'house' is the definition.
(I know that house can be written as dynasty)
'decay gutted and filthy' is the wordplay.
'gutted' says to hollow out the word (remove centre letters) (to gut something is to remove its insides).
'and' means one lot of letters go next to another.
'filthy' becomes 'nasty' (synonyms).
'decay' with its centre taken out is 'dy'.
'dy'+'nasty'='DYNASTY'
'in' is the link.
(Other definitions for dynasty that I've seen before include "Line of kings" , "Succession of rulers from one family" , "show" , "Series of hereditary rulers" , "Family line of rulers" .)