Clue: Mysterious affair, yeti? Mysterious place (4,5-3)
Answer: AREA FIFTY-ONE
Explanation: Definition: Mysterious place
(AFFAIR YETI)* gives AREA FIFTY, with an I left over for the ONE – usually written Area 51, this is a US Air Force secret facility, linked with a number of conspiracy theories about UFOs, particularly the so-called Roswell Incident