Re-attaching leather

is that a sedan chair?

as long as we're here, let me freeload on this topic, with a question that will probably come up with a similar answer. I have an Egyptian tambourine with a head, probably some sort of thin rawhide, held on with some sort of glue (no nails). About a quarter of the head has come loose from the body (the body has some really neat bone and shell geometrical tiling around it, so I'd like to restore it).

Someone acouple years ago suggested I use some sort of glue, but I can't remember what. I suspect I should also wet the leather, which should stretch it a bit, since it probably shrunk as it dried when they made it, which would have made it a taut drumhead, but it's now too small unwetted to fit around the rim of the head. Any ideas on the kind of glue?

I would suspect that wetting the leather to stretch it (which might be problematic with gilding), some sort of glue, and some sort of nails with decorative heads would be involved in repairing the chair too.

Any leather experts around?