We hear less important parts of pop singles, moreover (7)
I believe the answer is:
besides
'moreover' is the definition.
('besides' can be a synonym of 'moreover')
'we hear less important parts of pop singles' is the wordplay.
I cannot really understand how this works, but
'parts' could be 'sides' (side is a kind of part) and 'sides' is found in the answer.
The remaining letters 'be' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
(Other definitions for besides that I've seen before include "Moreover" , "See bids (anag)" , "Additionally" , "also is available" , "What's more" .)