Ten years after the death of Hepzibah Smith, Voldemort returns to Hogwarts, ostensibly to ask Dumbledore for a teaching job. Dumbledore refuses. He then curses the Defence Against the Dark Arts position, and since that day, no professor has stayed for more than one year in that post. Voldemore’s true purpose for the visit was to hide one of his Horcruxes — the Diadem of Ravenclaw — inside the Room of Requirement.
At this meeting, Voldemort’s appearance has changed:
[H]e was no longer handsome Tom Riddle. It was as though his features had been burned and blurred; they were waxy and oddly distorted, and the whites of the eyes now had a permanently bloody look, though the pupils were not yet the slits that Harry knew they would become. He was wearing a long black cloak, and his face was as pale as the snow glistening on his shoulders (HBP20).
Tom Riddle worked for Borgin and Burkes for over ten years, at the end of which he murdered Hepzibah Smith, framed her house-elf for the murder, and stole Hufflepuff's cup and Slytherin's locket. Dumbledore describes what followed thus:
"Ten years separates Hokey’s memory and this one, ten years during which we can only guess at what Lord Voldemort was doing. . . ." (HBP20)
After those ten years pass, Voldemort comes to visit Dumbledore and ask about taking up a teaching post. Since it is ten years after Smith's death, it takes place around 1966 or 1967.