Unsuitable at home, exotic pet (5)
I believe the answer is:
inept
'unsuitable' is the definition.
(thesaurus)
'home exotic pet' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'exotic' is an anagram indicator.
'pet' is an anagram of 'ept'.
'in'+'ept'='INEPT'
'at' acts as a link.
(Other definitions for inept that I've seen before include "Hopelessly incapable" , "Unskilful or unsuitable" , "Blundering" , "Clumsy, out of place" , "Incompetent and ineffectual" .)