Classic ship in the past seen around river (4)

I believe the answer is:
argo
'classic ship' is the definition.
'Argo' can be an answer for 'ship' (ship in Greek myth). I'm not sure about the 'classic' bit.
'past seen around river' is the wordplay.
'past' becomes 'ago' (similar in meaning).
'seen around' means one lot of letters goes inside another.
'river' becomes 'r' (abbreviation).
'ago' placed around 'r' is 'ARGO'.
'in the' is the link.
Can you help me to learn more?
(Other definitions for argo that I've seen before include "Ship in which Jason searched for the Golden Fleece" , "Old ship" , "Old craft" , "Old sailing vessel" , "Ancient ship" .)