Become liable for debts without interest? (9)
I believe the answer is:
incurious
'without interest?' is the definition.
(I've seen this before)
'become liable for debts' is the wordplay.
'become liable for' becomes 'incur' (I've seen this before).
'debts' becomes 'IOUs' (promises to pay debts).
'incur'+'ious'='INCURIOUS'
(Other definitions for incurious that I've seen before include "Lacking inquisitiveness" , "without interest" .)