First person in jazz to make three-note chord (5)
I believe the answer is:
triad
'chord' is the definition.
(triad is a kind of chord)
'first person in jazz' is the wordplay.
'first person' becomes 'I' (first-person pronoun).
'in' is an insertion indicator.
'jazz' becomes 'trad' (trad jazz is a type of jazz).
'i' put into 'trad' is 'TRIAD'.
'to make three-note' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for triad that I've seen before include "Up to date" , "trio" , "Union of three" , "Criminals" , "Group or set of three" .)