Night flier on the staff (5)
I believe the answer is:
'the staff' is the definition.
(I've seen this before)
'night flier on' is the wordplay.
'night flier' becomes 'bat' (I've seen this before).
(Other definitions for baton that I've seen before include "A conductor wields it - or a policemen" , "Conductor's wand" , "Controller of players" , "weapon" , "Short rod (that can be passed!)" .)