Carthaginian leader beheaded man-eater on horse (8)
I believe the answer is:
hannibal
'carthaginian leader' is the definition.
(ancient general of Carthage)
'beheaded man-eater on horse' is the wordplay.
'beheaded' means to remove the first letter (the head of the word is removed).
'man-eater' becomes 'cannibal' (synonyms).
'on' is a charade indicator (letters next to each other).
'horse' becomes 'h' (synonyms).
'cannibal' with its first letter taken off is 'annibal'.
'annibal' after 'h' is 'HANNIBAL'.
(Other definitions for hannibal that I've seen before include "Carthaginian general who crossed the Alps to defeat Rome" , "Famous general who crossed the Alps with elephants and defeated the Romans" , "Carthaginian general who fought Rome" , "Carthaginian general who crossed Alps to attack Rome" , "Great Carthaginian general who led army over the Alps against Rome" .)