Greek hero essentially American (7)
I believe the answer is:
perseus
'greek hero' is the definition.
(I've seen this before)
'essentially american' is the wordplay.
'essentially' becomes 'per se' (I've seen this in other clues).
'american' becomes 'US' (abbreviation for United States).
'perse'+'us'='PERSEUS'
(Other definitions for perseus that I've seen before include "'Having slain Medusa, he became a constellation (7)'" , "Group of stars" , "He beheaded Medusa" , "Son of Zeus" , "Greek hero who rescued Andromeda" .)