Do back debts; that’s disgusting (6)
I believe the answer is:
odious
'disgusting' is the definition.
(I've seen this in another clue)
'do back debts' is the wordplay.
'back' says the letters should be written in reverse.
'debts' becomes 'IOUs' (promises to pay debts).
'do' back-to-front is 'od'.
'od'+'ious'='ODIOUS'
'that's' is the link.
(Other definitions for odious that I've seen before include "Ghastly" , "Really hateful, detestable" , "Contemptible" , "Detestable, execrable" , "Unpleasant, repulsive" .)