Offensive, getting overdrawn on top of debts (6)
I believe the answer is:
odious
'offensive' is the definition.
(thesaurus)
'overdrawn on top of debts' is the wordplay.
'overdrawn' becomes 'od'.
'on top of' means one lot of letters go next to another.
'debts' becomes 'ious'.
'od'+'ious'='ODIOUS'
'getting' is the link.
(Other definitions for odious that I've seen before include "Contemptible" , "Hateful, really nasty" , "Vile" , "Extremely unpleasant" , "Loathsome and repulsive" .)