To the doctor, one introducing the right instrument (8)
I believe the answer is:
trombone
'instrument' is the definition.
(trombone is a kind of instrument)
'to the doctor one introducing the right' is the wordplay.
'the doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'introducing' means one lot of letters goes inside another (some letters introduced or inserted into others).
'the right' becomes 'r' (common abbreviation).
'to'+'mb'+'one'='tombone'
'tombone' going around 'r' is 'TROMBONE'.
(Other definitions for trombone that I've seen before include "play this" , "Brass instrument with sliding tubes" , "source of notes" , "Brass band instrument" , "Blow me!" .)