He defeated Gore; he bugs Gore terribly (6,4)

I believe the answer is:

george bush

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'he defeated gore' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'he bugs gore terribly' is the wordplay.
'terribly' indicates an anagram.
'he'+'bugs'+'gore'='hebugsgore'
'hebugsgore' with letters rearranged gives 'GEORGE BUSH'.

Can you help me to learn more?

(Another definition for george bush that I've seen is " President".)

I've seen this clue in The Everyman puzzle in The Observer.

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