Go down with a great story (4)
I believe the answer is:
saga
'story' is the definition.
(saga is a kind of story)
'go down with a great' is the wordplay.
'go down' becomes 'sa' (I can't justify this - if you can you should give a lot more credence to this answer).
'with' means one lot of letters goes inside another.
'great' becomes 'g' (abbreviation in place names).
'a'+'g'='ag'
'sa' enclosing 'ag' is 'SAGA'.
Can you help me to learn more?
(Other definitions for saga that I've seen before include "Account of great heroism" , "Epic tale" , "Long narrative" , "Body of legend" , "Heroic narrative" .)