The last original KY elk disappeared during the Civil War. The restoration of elk in KY began with the release of 7 Kansas elk in December, 1997. Over the next four years another 1,542 wild elk from UT, AZ, ND, OR, and NM were rleased in a 3,000,000 acre of eastern Ky.
We started hunting these elk with 6 tags in 2001. These days 800-1,000 permits are issued by lottery each fall. The herd is estimated to contain 10,000-12,000 animals now.
Last year 32,000 people applied. Nonresidents may apply for the same prices as residents - $10. A computer will draw the permits with "no more than 10% being allocated to nonresidents". If a person is drawn then they buy the elk license. Hunter success is generally around 76%.
I've applied since 2007 when I retired from the dept.