Southern state utterly into bondage (7)
I believe the answer is:
slavery
'bondage' is the definition.
('slavery' can be a synonym of 'bondage')
'southern state utterly' is the wordplay.
'southern' becomes 's' (abbreviation).
'state' becomes 'la' (abbreviation for Louisiana).
'utterly' becomes 'very'.
's'+'la'+'very'='SLAVERY'
'into' is the link.
(Other definitions for slavery that I've seen before include "Extreme drudgery" , "Bondage" , "State of subjugation" .)