The first thing to do is to get all of the old glue off. I would then glue with West System epoxy mixed with microfibres and some yellow ochre and brown umber.
You can buy a small kit of west system like the one below.
If you cannot find small quantities of ochre near you let me know and I will pop some in the post to you.
Once you have the old glue off mix the west system with the ochre and using a sacrificial small brush, brush the glue onto the exposed end grain then using a heat gun or hairdryer heat the glue and you will see it sink into the end grain. Wax the whole piece with a clear paste wax around the join wipe extra wax with your finger being careful not to get any in the break. (this will prevent any excess glue sticking to the 'show' surface) Then mix the remaining glue with the microfibres until you have a paste like consistency, apply this mix to the join then clamp together. I would suggest clamping each piece onto a board covered in plastic or coated in a paste wax then clamp the two pieces together. Make sure you have a good join with everything lined up, clean off the excess glue with acetone. When that is all dried you can then replace the broken spline as Aidan suggested.
Good luck, it is a lovely piece and well worth the effort.
https://www.amazon.co.uk/Epoxy-Resi...XKMF209EQF2&psc=1&refRID=HGVZMT80PXKMF209EQF2