Greek hero is due, so running around unknown ship (8)
I believe the answer is:
odysseus
'greek hero' is the definition.
(I've seen this in another clue)
'due so running around unknown ship' is the wordplay.
'running' is an anagram indicator.
'around' indicates putting letters inside.
'unknown' becomes 'y' (algebra).
'ship' becomes 'SS' (prefix in ship names eg SS Great Britain).
'due'+'so'='dueso'
'dueso' is an anagram of 'odeus'.
'y'+'ss'='yss'
'odeus' enclosing 'yss' is 'ODYSSEUS'.
'is' acts as a link.
(Other definitions for odysseus that I've seen before include "Ancient king" , "Classical traveller" , "Homeric wanderer" , "character on an epic journey" , "Homer's mythical Greek hero" .)