Dog carrying stick around at home (6)
I believe the answer is:
canine
'dog' is the definition.
(thesaurus)
'stick around at home' is the wordplay.
'stick' becomes 'cane' (cane is a kind of stick).
'around' means one lot of letters goes inside another.
'at home' becomes 'in' ('in' can be similar in meaning to 'at home').
'cane' going around 'in' is 'CANINE'.
'carrying' is the link.
(Other definitions for canine that I've seen before include "Pointed conical tooth" , "Dog-like" , "Doggy; tooth" , "Maybe setter" , "such as Lassie" .)