The most common and most likely answer to this crossword clue is the 9 letter word EXPURGATE
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More clues leading to the result EXPURGATE
Buddy explains!

The straight part
We know that "censor" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case censor = expurgate.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 EXPURGATE mean?
EXPURGATE verb- To edit out (incorrect, offensive, or otherwise undesirable information) from a book or other publication; to cleanse; to purge.
- To undertake editing out incorrect, offensive, or otherwise undesirable information from (a book or other publication); to cleanse; to purge.