What you've described is a check in the board and checking is not the result of normal expansion/contraction, per se, of the wood. Checking is the result of opposing forces/stresses in the wood, causing the splitting. Your problem is not the result of expansion /contraction. Sometimes gluing and clamping will "fix" the checking, sometimes not.
I'm supposing your table is more of a general utility or moderate quality piece, and not a high-end heirloom type piece.
I suspect no glue... and reclamping... will resolve that checking problem. I would clean the gap, of old glue, and insert carved slivers of wood, to fill the gap, being careful not to force the slivers, too hard, into the gap.... you wouldn't want to pry the gap further apart. Do some dry fits, for best fitting. Prior to applying glue to the slivers, apply a coat of finish onto the (pending table) face surfaces of the slivers, to prevent the glue from adhereing to those surfaces. The slivers should be oversized, to later trim/sand level/smooth with the table surface.
If the "sliver fix" is impractical for your circumstances, i.e., the gap is too small for reasonable insertion of slivers, then your next most reasonable option may be to use an epoxy as a filler, unless something like Famowood wood filler can be matched (color) to the table.
Prior to building the table, the boards should have been acclimated, first, then used for the construction, but that may have been attempted as best as could be, at the time. Checking is fairly often seen in older construction, especally in construction with wide boards, planks and panels.