Great leader raised new hatchet to cut tree (9)

I believe the answer is:
alexander
'great leader' is the definition.
The definition and answer can be both people as well as being singular nouns.
Perhaps there's a link between them I don't understand?
'raised new hatchet to cut tree' is the wordplay.
'raised' shows that the letters should be reversed in order (going up in a down clue).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'hatchet' becomes 'axe' (hatchet is a type of axe).
'to cut' indicates putting letters inside (some letters cut their way into a word).
'tree' becomes 'alder' (alder is a kind of tree).
'n'+'axe'='naxe'
'naxe' back-to-front is 'exan'.
'exan' going inside 'alder' is 'ALEXANDER'.
Can you help me to learn more?
(Other definitions for alexander that I've seen before include "Ancient king of Macedon" , "Great king; --- Pope, poet" , "Name of Pope" , "Great Greek military commander" , "Macedon's "great" king, d. 323 BC" .)
