Outcast's song in public house (6)
I believe the answer is:
pariah
'outcast's' is the definition.
(synonyms)
'song in public house' is the wordplay.
'song' becomes 'aria' (aria is a kind of song).
'in' is an insertion indicator.
'public house' becomes 'ph' (abbreviation).
'aria' going into 'ph' is 'PARIAH'.
(Other definitions for pariah that I've seen before include "Person despised and rejected by society" , "Small box for valuables" , "Outcast (dog)" , "Unacceptable person" , "Person ostracised by society" .)