National hero backing King Edward's assassin (8)
I believe the answer is:
murderer
'assassin' is the definition.
(I've seen this before)
'national hero backing king edward's' is the wordplay.
'national hero' becomes 'red rum' (horse that won the Grand National three times).
'backing' says the letters should be written backwards.
'king edward' becomes 'er' (abbreviation for Eduardus Rex).
'redrum' written backwards gives 'murder'.
'murder'+'er'='MURDERER'
(Other definitions for murderer that I've seen before include "One commits homicide" , "hit man" , "Deliberate unlawful killer" , "Criminal killer" , "Assassin" .)