Old application for river (4)
I believe the answer is:
ouse
'for river' is the definition.
(Yorkshire river)
'old application' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'application' becomes 'use' (I've seen this in other clues).
'o'+'use'='OUSE'
(Other definitions for ouse that I've seen before include "Norfolk river" , "Flowing water" , "York's river" , "O, Sue, here is a river" , "Name of river in Sussex or Yorkshire" .)