Species Native or Naturalized in the Continental US
With a few exceptions, diet will determine whether a species requires a permit. If the species is herbivorous, omnivorous, or detritivorous, then permits, likely ones stipulating a containment facility, would be required. A few strictly carnivorous species will not require permits. I was specifically given the “all-clear” for interstate transport of Neobarrettia spinosa, a large carnivorous katydid native to Texas.
Importation or Possession of Exotic Species in the Continental US
All exotic species of Orthoptera will require stringent USDA permit conditions and a containment facility. Even if you are able to obtain the permits to import, then also check with the FWS as a FWS permit is required to import any animal (exemptions for personal pets may apply).