Instrument that’s not broken, but odd bits missing (4)
I believe the answer is:
oboe
'instrument' is the definition.
(type of musical instrument)
'not broken but odd bits missing' is the wordplay.
'but odd bits missing' indicates alternate letters (letters in odd-numbered positions removed).
'not'+'broken'='notbroken'
The alternate letters of 'notbroken' are 'OBOE'.
'that's' is the link.
(Other definitions for oboe that I've seen before include "Double-reed wind instrument" , "Double-reeded woodwind instrument" , "Musical instrument" , "issuer of notes" , "music producer" .)