Re: bigger picture *LINK*
Sgian Dubh
As David suggested you could use a pocket screw, something like as shown below, or similar - there are a pocket screw guides, screws and drivers available as an alternative, e.g. https://www.axminstertools.com/ujk-technology-mini-pocket-hole-jig-kit-101603 Form the pocket first in the side of the divider where the drawer runners are located. The resulting repair will eventually be hidden by the drawer.

Then, as Bill suggested, clamp across from the cabinet top to the bottom panel centring the clamp on the front edge of the divider to close the gap. Insert a screw to hold the housing joint tight. Remove the clamp to check the pocket hole and screw can actually close the joint effectively. If not, add one or two more pocket holes and dry clamp again, adding more screws.
When you find you can hold the joint tight with just screws in the pocket holes, go through the whole exercise again, but this time add an adhesive, where my choice would be an epoxy resin. Prior to adding an adhesive, you may find you can clean off some of the existing glue, and if possible to do so without opening the joint further, I'd do so.
It might also be a good idea to put pocket screws front and back because the joint may have been weakened along its whole length. Slainte.
Pocket hole jig kit