It's not that ancient history is incomplete (4)
I believe the answer is:
this
'it's not that' is the definition.
(this one as opposed to that one)
'ancient history is incomplete' is the wordplay.
'is incomplete' indicates a hidden word (an incomplete sample of the clue).
'THIS' can be found hidden inside 'ancient history'.
(Other definitions for this that I've seen before include "The thing here referred to" , "One particular" , "The thing under discussion" , "What's here" , "near thing" .)