Quite a problem for listeners! (4)
I believe the answer is:
some
'quite a' is the definition.
('that's some car!' means 'that's quite a car!')
'problem for listeners' is the wordplay.
'problem' becomes 'sum' (as in a mathematical problem).
'for listeners' indicates a 'sounds like' (homophone) clue.
'sum' is a homophone of 'SOME'.
(Other definitions for some that I've seen before include "Hard work" , "Undefined number" , "Unknown or unspecified amount or number" , "A little; not a little" , "certain" .)