On the house that's detached (4)
I believe the answer is:
free
I believe this clue is a double definition.
'on the house' is the first definition.
(something on the house is given away free)
'detached' is the second definition.
(thesaurus)
'that's' is the link.
(Other definitions for free that I've seen before include "Release; without cost" , "Not working" , "Exempt" , "Complimentary" , "Not fixed; not in use" .)