Small rodent heading off for river (4)
I believe the answer is:
ouse
'for river' is the definition.
(Yorkshire river)
'small rodent heading off' is the wordplay.
'small rodent' becomes 'mouse' (I've seen this before).
'heading off' means to remove the first letter.
'mouse' with its initial letter taken off is 'OUSE'.
(Other definitions for ouse that I've seen before include "Name of river in Sussex or Yorkshire" , "N English river (and S English river)" , "River of 1 across" , "Norfolk river" , "Runner" .)