Run up, as expenses (5)
I believe the answer is:
incur
'run up as expenses' 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" , "Provoke" , "Become liable to (something) through one's actions" , "Become responsible for" , "Arouse" .)