Because the NBC ID on the photo back was incomplete, I conducted a copyright search. NBC registered only one photo for the years 1965-1969-a color slide from Bonanza of Ben Cartwright on a horse.
Nothing turned up when I searched "Star Trek" for the years 1965 through 1969 in either film or artwork.
There's no evidence this photo was ever under copyright.
Note that it may still be copyrighted in jurisdictions that do not apply the rule of the shorter term for US works (depending on the date of the author's death), such as Canada (50 p.m.a.), Mainland China (50 p.m.a., not Hong Kong or Macao), Germany (70 p.m.a.), Mexico (100 p.m.a.), Switzerland (70 p.m.a.), and other countries with individual treaties.