About the only thing I can think of, aside from re-making the apron, would be to plane the flat edges of the circular top back to the edge of the apron. If the apron is screwed in place (looks possible from the picture) you could unscrew it and move it to the edge. Typically these will have glue blocks and glue in addition to screws, which would make disassembly a challenge. Do the leaves have an apron attached? You'd want to be sure they still fit.

If it were mine I'd put a tablecloth on the table and forget about it.

Thank you for the response. The extra leaf has an apron and it seems to be better aligned with the edge of the leaf than it is on the table itself.

I have looked at other tables I have in the house and they appear to have a piece of flat molding covering the gap. But I'm not sure how that would work or be attached in the case where you have an extra leaf.

I vote for the tablecloth, too.

It looks like there are alignment pegs sticking out of the apron. If so, you can't cover them up without messing with the leaf insertion.

That gap needs to be there. In winter, the wood top can shrink as much as 3/8" across the grain. If the aprons met, it would leave a gap between the two table halves. The solution which most table manufacturers have adopted, are the "gap covers" as you have seen on the other tables in your home. You could use a piece of door astragal moulding or something similar, finish to match the aprons and just tack to ONE side of the apron with brads. You would do the same for the gap between the two leaves.

They could have as easily planned for the shrinkage at the extreme edges of the tabletop, making the apron ends a fixed point. So I fail to see the logic.

Casey