One grabs a few notes here, in the middle (8)
I believe the answer is:
snatcher
'one grabs' is the definition.
(I know that a snatcher grabs)
'a few notes here in the middle' is the wordplay.
'a few notes' becomes 'snatch' (snatch can mean a bit of music).
'in the middle' says to take the centre.
The central letters of 'here' are 'er'.
'snatch'+'er'='SNATCHER'
(Other definitions for snatcher that I've seen before include "Stealer; kidnapper" , "Person grabbing" , "Thief" , "One seizing suddenly" , "See 1" .)