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They make metal clips with grip material on them that slip over the hoop where the bass drum pedal attaches to prevent clamp damage to the wooden hoop. Possibly you could use one to bridge the repaired seam. It would hide the seam, add strength, and the pedal clamp pressure would even help hold it together.

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All hoops are like barrel hoops they are glued and clamp some little brads to hold in place

Sorry for taking to long to edit

Elmers pro wood glue. I repeated two Slingerland hoops that had separated . Glued them, clamped them together, and let sit a couple days. Strong as ever. You can use Saran Wrap if needed under your clamps so they don't stick to anything.

If you use yellow PVA (poly vinyl acetate) glue, the joint will probably be fine. These are common woodglues: Elmers, Titebond. If it were a clean break, as if it had been cut, you’d probably be out of luck, since there would only be end-grain to join together. End grain is the weakest part of any joining process, be it glue or screws. But since you have the overlapping “puzzle piece” joint, the glue will have some long grain to make a solid connection.

A band clamp would work well, or you could clamp blocks on either side of the joint, a few inches from the break, and then carefully run two clamps, one inside and one outside the hoop, from block to block to draw the joint together. If this doesn’t make sense, let me know and I’ll mock up the joint and shoot a photo of it.

Use a liberal amount of glue and just clean up the squeeze-out. Masking tape near the joint will help the clean-up.

Jeff (jccabinets) may chime in. Gluing wood is his biz!

Josh