Formally Addressing the Former President
When addressing a former President of the United States in a formal setting, the correct form is “Mr. LastName.” (“President LastName” or “Mr. President” are terms reserved for the current head of state.) This is true for other ex-officials, as well. When talking about the person to a third party, on the other hand, it’s appropriate to say, “former President LastName.” This holds for introductions, as well: A current state governor is introduced as “Governor Tom Smith,” while you’d introduce an ex-governor as “former Governor Jim Bell.”
Informally Addressing the Former President
Now, let’s look a little closer. In an informal setting (such as a private lunch), it’s acceptable to use the title the ex-official held. Here, you could refer to former President Jimmy Carter as either “President Carter” or “Mr. Carter.” In reality, many people ignore this convention and refer to former Presidents as "President Last Name" when they are in settings where nearly everyone would afford them the honor of the title. Technically, this is still incorrect but there are enough former Presidents allowing this that it has become a somewhat common mistake.
https://emilypost.com/advice/addressing-a-former-president-of-the-united-states
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I don’t love it. But if they’d said, “Former President Trump,” every time they addressed him in the debate, it would have taken up even more time. And I think the form is changing over time — I hear, “President Obama,” often.
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