Doctor engaged in weary tone (6)
I believe the answer is:
timbre
'tone' is the definition.
(I've seen this before)
'doctor engaged in weary' is the wordplay.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'engaged in' indicates putting letters inside.
'weary' becomes 'tire' (I've seen this before).
'mb' put into 'tire' is 'TIMBRE'.
(Other definitions for timbre that I've seen before include "Tone of voice - sounds wooden" , "Sound's character" , "Characteristic voice sound" , "Musical tone quality" , "colour we hear" .)