Clue: Mysterious affair seen briefly coming over in profundity? (12,6,6)
Answer: UNIDENTIFIED FLYING OBJECT
Explanation: Definition: Mysterious affair seen briefly coming over
UFO is hidden in the reverse of prOFUndity – I'm not keen on this type of clue, where the wordplay isn't much help until you've found the answer: fortunately I guessed this one early on, largely from the B of OBJECT