"Alfred" and "Judith" composer (4)
I believe the answer is:
'alfred and judith composer' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for arne that I've seen before include "Thomas --, composer of Rule, Britannia!" , "Rule Britannia's composer, d. 1778" , "Rule, Britannia author" , "Rule Britannia composer, d. 1778" .)