The most common and most likely answer to this crossword clue is the 7 letter word ATHEIST
I've seen this crossword clue in The Times
A
T
H
E
I
S
T
More clues leading to the result ATHEIST
- Seeing a crime being committed possibly, but not believing
- I don’t believe a chap who thinks God exists
- One not believing in being at scene of crime
- Who believes there is no God witnessing crime?
- One doesn't believe in theft
- Faithless sort cheers up on the job
- One doubts God is involved in robbery
- He’s unconvinced that he is taking part
- Sceptic engaged in armed robbery?
- He can’t believe that he is taking part in this
Buddy explains!

The straight part
We know that "One not believing in being" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one not believing in being = atheist.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 ATHEIST mean?
ATHEIST noun- A person who does not believe in deities.
- A person who does not believe in a particular deity (or any deity in a particular pantheon), notwithstanding that they may believe in another deity.
- Of or relating to atheists or atheism; atheistic.