German composer I overlooked successfully (4)
I believe the answer is:
well
'successfully' is the definition.
(I've seen this in other clues)
'german composer i overlooked' is the wordplay.
'german composer' becomes 'Weill' (Kurt Weill, 1900-1950).
'overlooked' is a deletion indicator.
'weill' with 'i' taken away is 'WELL'.
(Other definitions for well that I've seen before include "We shall" , "Very; deep shaft" , "Lift-shaft" , "indeed" , "Very much; plentiful source or supply" .)