The most common and most likely answer to this crossword clue is the 4 plus 6 letter word BLUE PENCIL
I've seen this crossword clue in Financial Times
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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 = blue pencil.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 BLUE PENCIL mean?
BLUE PENCIL verb- To edit, especially to censor, written documents.
- To use a line-item veto.