Music maker, oddly overlooked, but keen (3)
I believe the answer is:
uke
'music maker' is the definition.
(uke is a kind of musical instrument)
'oddly overlooked but keen' is the wordplay.
'oddly overlooked' means one should take alternating letters.
'but'+'keen'='butkeen'
The alternate letters of 'butkeen' are 'UKE'.
(Other definitions for uke that I've seen before include "George Formby's instrument (abbr)" , "Music producer" , "Notes producer sometimes plucked" .)