PocketShot is a commercially available brand of circular slingshot, an evolution of the glove slingshots you may have seen in school. PocketShots comprise two main parts - a plastic handle, and a latex pouch. This model is a printable version of the plastic handle parts. To complete it you'll need a rubber pouch, which you can buy as spare parts from stores carrying the PocketShot.
Inner part should be printed in a strong material with a high infill. Outer and Cap parts can be printed in standard way.
Make sure to smooth down the areas around where the latex pouch is likely to touch, to reduce abrasion and improve life of pouch.
Photographic references of the original product, with design elements adjusted to be printable without supports.