Slump on sofa at last for a story (4)
I believe the answer is:
saga
'story' is the definition.
(a saga is a long story)
'slump on sofa at last' is the wordplay.
'slump' becomes 'sag' (I've seen this in another clue).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'at last' suggests the final letters.
The last letter of 'sofa' is 'a'.
'sag'+'a'='SAGA'
'for a' is the link.
(Other definitions for saga that I've seen before include "A long adventurous story - it's a gas" , "Old story" , "Tale of heroes" , "Lengthy tale" , "Long heroic, family, story" .)