Joan's going out with Argonauts' leader (5)
I believe the answer is:
jason
'argonauts' leader' is the definition.
(I've seen this before)
'joan's going out' is the wordplay.
'going out' is an anagram indicator (out can mean wrong or inaccurate).
'joans' with letters rearranged gives 'JASON'.
'with' acts as a link.
(Other definitions for jason that I've seen before include "Chief Argonaut" , "Greek hero, captain of the Argo" , "Argonaut captain" , "Greek hero, leader of the Argonauts" , "Argonaut leader" .)