Animal that's right at home in house (5)
I believe the answer is:
rhino
'animal' is the definition.
(I've seen this before)
'right at home in house' is the wordplay.
'right' becomes 'r' (common abbreviation).
'at home' becomes 'in' ('in' can be similar in meaning to 'at home').
'in' is an insertion indicator.
'house' becomes 'ho' (abbreviation for house).
'in' inserted into 'ho' is 'hino'.
'r'+'hino'='RHINO'
'that's' is the link.
(Other definitions for rhino that I've seen before include "Hi, Ron, this animal is abbreviated" , "Hi, Ron! (anag)" , "Thick-skinned animal (abbr) - money (slang)" , "chargeable > 11 [LOLLY]?" , "one might charge in Africa" .)