Short ballad penned by a writer in World's End (10)
'world's end' is the definition.
(the end of the world)
'short ballad penned by a writer in' is the wordplay.
'short' means to remove the last letter.
'ballad' becomes 'calypso' (I've seen this before).
'penned by' indicates putting letters inside.
'writer in' becomes 'poe' (I can't justify this - if you can you should believe this answer much more).
'calypso' with its final letter removed is 'calyps'.
'calyps' put inside 'apoe' is 'APOCALYPSE'.
(Other definitions for apocalypse that I've seen before include "terrible event", "End of the world", "the last item", "Catastrophic event", "This last book".)