NCC-1697 was the registry number of a 23rd century Federation starship operated by Starfleet. This unnamed starship underwent a layover at Starbase 11 in 2267. The ship's number was seen on a chart indicating the repair status of several vessels. (TOS: "Court Martial")
This ship was only identified by its hull number. According to the Star Trek Encyclopedia, which was in turn, based on Greg Jein's 1975 "The Case of Jonathan Doe Starship"-article, this registry was assigned to the Constitution-class heavy cruiser USS Essex.
The Star Trek Encyclopedia made reference to a USS Essex, registry NCC-1697, as listed among the Constitution-class starships commissioned by Starfleet. That ship was actually mentioned in an early draft shooting script for TOS: "Journey to Babel",  and concurrently included in internal memos from D.C. Fontana and Robert Justman, suggesting lists of possible Constitution-class starship names to consider for use in The Original Series. These lists, published in The Making of Star Trek (pp. 164-165), were used to match Essex with the registry NCC-1697 that appeared on the wall chart seen in "Court Martial" by Jein in his article.
This information was later endorsed and adapted for use in the Encyclopedia by author, later friend and co-worker Mike Okuda, without ever explicitly citing a canon source, but emphatically acknowledging Jein's article, which thereby became the only unofficial source referenced in the Encyclopedia. (1st ed., pp. 56-57; 3rd ed., pp. 85-86) Another starship named USS Essex (NCC-173) did eventually show up in canon.