First author researcher on a manuscript left job without publishing A grant-funded researcher wrote a manuscript that they were first author on. All co-authors were awarded time to make edits. Before getting departmental approval for submitting to publication, the grant-funded researcher started a new job. Considerable time passed before departmental approval was awarded.
The original first author has expressed concern that they will not have time to work on the old manuscript because they started a new job. However, the PI for the grant (and co-author on the paper) wishes to publish the manuscript. The PI has stated if minimal to no edits are required, the authorship order would remain the same. If the slightly outdated paper comes back from review with a decent amount of edits to be made, potentially new portions of analysis, while the first author states that they do not have time to work on the old manuscript, can one of the co-authors potentially take over as first author? Does the original first author have to give consent? Keep in mind that the manuscript is already written up.
In the field which the manuscript is written, it is generally accepted that authorship order is determined by amount of effort involved for each author.
If the slightly outdated paper comes back from review with a decent amount of edits to be made, potentially new portions of analysis, while the first author states that they do not have time to work on the old manuscript, can one of the co-authors potentially take over as first author?

Potentially, yes. Far from a guarantee. Probably the old first author would become second or co-first, depending on norms in your field.

Does the original first author have to give consent?

Yes. In fact, everyone has to agree to the new order, even if their relative position is unchanged.