Weary about doctor’s tone of voice (6)
I believe the answer is:
timbre
'tone of voice' is the definition.
(thesaurus)
'weary about doctor's' is the wordplay.
'weary' becomes 'tire' (synonyms).
'about' means one lot of letters goes inside another.
'doctor' becomes 'MB' (Bachelor of Medicine).
'tire' enclosing 'mb' is 'TIMBRE'.
(Other definitions for timbre that I've seen before include "Distinctive tone" , "Sound's character" , "Ring" , "Quality of musical sound" , "Musical tone quality" .)