It's an honour to hold doctor's second instrument (4)
I believe the answer is:
oboe
'instrument' is the definition.
(type of musical instrument)
'it's an honour to hold doctor's second' is the wordplay.
'it's an honour' becomes 'OBE' (Order of the British Empire award).
'to hold' is an insertion indicator.
'doctor's second' becomes 'o' (2nd letter of 'doctor').
'obe' placed around 'o' is 'OBOE'.
(Other definitions for oboe that I've seen before include "Reed instrument" , "Double-reed woodwind" , "source of notes" , "Orchestral piece" , "Source of music" .)