Out to boo the first musician (6)
I believe the answer is:
oboist
'musician' is the definition.
(I know that oboist is a type of musician)
'out to boo the first' is the wordplay.
'out to' indicates anagramming the letters.
'the first' becomes 'ist' (ist resembles 1st).
'boo' anagrammed gives 'obo'.
'obo'+'ist'='OBOIST'
(Other definitions for oboist that I've seen before include "Do I boost the musician?" , "orchestra member" , "Wind player" , "Instrumentalist" , "Musician who plays woodwind of treble pitch" .)