Weary about doctor's tone (6)
I believe the answer is:
timbre
'tone' is the definition.
(synonyms)
'weary about doctor's' is the wordplay.
'weary' becomes 'tire' (synonyms).
'about' indicates putting letters inside.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'tire' going around 'mb' is 'TIMBRE'.
(Other definitions for timbre that I've seen before include "Musical tone quality" , "Tone of voice - sounds wooden" , "Quality of sound of the voice" , "Quality of musical sound" , "Characteristic quality of sound" .)