The most common and most likely answer to this crossword clue is the 9 letter word DISBELIEF
I've seen this crossword clue in The Daily Telegraph
D
I
S
B
E
L
I
E
F
More clues leading to the result DISBELIEF
- Doubt detectives contradict sheriff, ultimately
- Inspector’s complaint about core of policy causing incredulity
- Lack of faith shown by Delibes, I suspect, before start of fugue
- Suspicion that Lee's FBI ID has been compromised
- Doubt that cop’s boy corrupted file after consuming drug
- Dubiously feel bid is producing scepticism
Buddy explains!

The straight part
We know that "Lack of faith" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lack of faith = disbelief.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does DISBELIEF mean?
DISBELIEF noun- Unpreparedness, unwillingness, or inability to believe that something is the case.
- Astonishment.
- The loss or abandonment of a belief; cessation of belief.