Kirk's Voyage is a reference to the iconic science fiction television series Star TREK, which aired from 1966-1969. The main character of the show was Captain James T. KIRK, who commanded the USS Enterprise on a five-year mission of exploration and discovery. The term 'KIRK's Voyage' is often used to refer to this mission. The crossword solution for the term is TREK, which is an abbreviation of the show's title.