It's not unusual for a name to be preceded by an indefinite article in English, as in this example:
These are troubling times, but a President Barack Obama could handle them.
However, grammatically, the construction is odd because we combine the indefinite article a with the definite expression President Barack Obama, so you would expect this to lead to a semantic clash of sorts. However, it doesn't . We interpret the phrase a President Barack Obama to mean 'a person like President Barack Obama'.
But what about the following example, which I came across in a newspaper:
More specifically, a President Biden would confirm that a candidate who is unexciting but capable and conspicuously decent can win – especially during a crisis. (The Guardian, 17/10/20)
Here, as a reader, you would initially try to interpret this phrase in the same way as above, namely as 'a person like President Biden'. But that doesn't quite work when you realise that if the modalised would confirm is actualised after Biden's election, the phrase a President Biden is no longer appropriate, as he will then be President Biden. The very fact that he has become President then confirms (an unmodalised verb) that an unexciting candidate can win elections. The writer could not have used the phrase President Biden in his text, as that expression carries the presupposition that he has already been elected.
So what's going on here? I think that the writer of the Guardian sentence is trying to combine two authorial perspectives: the current perspective of the writer before the US elections (modalised, because we can't be sure what will happen), and the perspective he will have after Biden's election (unmodalised because it will be a fact).