Imagine not starting cryptic puzzle! (6)
I believe the answer is:
enigma
'puzzle' is the definition.
(I've seen this in another clue)
'imagine not starting cryptic' is the wordplay.
'not starting' means to remove the first letter.
'cryptic' is an anagram indicator (a cryptic or obscure order of the letters).
'imagine' with its first letter taken away is 'magine'.
'magine' is an anagram of 'ENIGMA'.
(Other definitions for enigma that I've seen before include "WW two Ger. code device; puzzle" , "Something mysterious and puzzling" , "It's mysterious like gamine" , "Mystery U puzzle" , "Mysterious person" .)