I don't think the North Korean leader would come to the White House and negotiate with the president Trump.
The American leader is either “President Trump” or “the American president”. I would omit “the” and capitalise “President”. When the title precedes the person’s name, it is capitalised.
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The American leader is either “President Trump” or “the American president”.
I would omit “the” and capitalise “President”.
When the title precedes the person’s name, it is capitalised. When it follows, as in “leader”, it is not necessary.