Run up, as debts (5)
I believe the answer is:
incur
'run up as debts' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for incur that I've seen before include "Bring on oneself, say costs" , "Fall into - invite" , "Invite, bring about" , "Meet" , "Become subject to (penalty)" .)