Bee, one going after doctor (5)
I believe the answer is:
drone
'bee' is the definition.
(I know that drone is a type of bee)
'one going after doctor' is the wordplay.
'going after' is a charade indicator (letters next to each other).
'doctor' becomes 'dr' (abbreviation).
'one' put after 'dr' is 'DRONE'.
(Other definitions for drone that I've seen before include "Buzzing sound" , "Queen bee1s mate" , "Monotonous sound - member of hive" , "Continuous sound; bee" , "Aeroplane" .)