Naughtily fool guy with mystery science (7)
I believe the answer is:
ufology
'mystery science' is the definition.
(study of UFOs)
'naughtily fool guy' is the wordplay.
'naughtily' indicates an anagram.
'fool'+'guy'='foolguy'
'foolguy' anagrammed gives 'UFOLOGY'.
'with' acts as a link.
(Other definitions for ufology that I've seen before include "Study of (supposedly) alien craft" , "Study of exotica" , "Formal study of flying saucers" , "Study of weird things in sky" , "Study of mysterious objects" .)