Musician beginning to thrill odd chap (9)
I believe the answer is:
trumpeter
'musician' is the definition.
(trumpeter is a kind of musician)
'beginning to thrill odd chap' is the wordplay.
'beginning to' suggests taking the first letters.
'odd' becomes 'rum' (I've seen this before).
'chap' becomes 'peter' (Peter is a man's name**).
The first letter of 'thrill' is 't'.
't'+'rum'+'peter'='TRUMPETER'
(Other definitions for trumpeter that I've seen before include "[SOMETHING FISHY]" , "It's the valve operator" , "Jumbo?" , "one of a band" , "Brass player" .)