Trendy blackguard has debts with no interest (9)
I believe the answer is:
incurious
'with no interest' is the definition.
(having no curiosity)
'trendy blackguard has debts' is the wordplay.
'trendy' becomes 'in' ('in' can mean fashionable).
'blackguard' becomes 'cur' (both can mean a dishonourable person).
'has' is a charade indicator (letters next to each other).
'debts' becomes 'IOUs' (promises to pay debts).
'in'+'cur'+'ious'='INCURIOUS'
(Other definitions for incurious that I've seen before include "Lacking inquisitiveness" , "without interest" .)