Instrument has nothing on tenor (4)
I believe the answer is:
oboe
'instrument' is the definition.
(oboe is a kind of instrument)
'has nothing on tenor' is the wordplay.
'has nothing' becomes 'o' (I've seen this in other clues).
'on' means one lot of letters go next to another.
'tenor' becomes 'boe' (singer Alfie Boe).
'o'+'boe'='OBOE'
(Other definitions for oboe that I've seen before include "bit of wind" , "Slender double-reed instrument" , "Player" , "Cor anglais in its family" , "source of notes" .)