Flying mammal on a stick (5)
I believe the answer is:
baton
'a stick' is the definition.
(term for a stick or staff)
'flying mammal on' is the wordplay.
'flying mammal' becomes 'bat' (I've seen this in another clue).
'bat'+'on'='BATON'
(Other definitions for baton that I've seen before include "Police (or conductor's) stick" , "It's used by a conductor and a policeman" , "Conductor wields it - or a policeman" , "Conductor's rod" , "Club, stick" .)