Imagine not beginning new puzzle (6)
I believe the answer is:
enigma
'puzzle' is the definition.
(I've seen this in another clue)
'imagine not beginning new' is the wordplay.
'not beginning' means to remove the first letter.
'new' is an anagram indicator.
'imagine' with its initial letter taken off is 'magine'.
'magine' anagrammed gives 'ENIGMA'.
(Other definitions for enigma that I've seen before include "Puzzle for gaming" , "Mysterious person/thing" , "'Puzzle, riddle (6)'" , "WWII cipher" , "Difficult problem" .)