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…Remember that she has an appointment.
…Remember she has an appointment.
We can always leave out the word that when it begins a clause and doesn’t really do anything in the clause. In neither of the sentences above is there a need for a comma. You certainly wouldn’t want a comma in the first one; the second one is exactly the same sentence.
If there is a dramatic pause after remember, you might use a colon and then cap the complete sentence. But a comma is not correct.