The most common and most likely answer to this crossword clue is the 11 letter word BLUE-PENCIL
I've seen this crossword clue in Financial Times
B
L
U
E
-
P
E
N
C
I
L
More clues leading to the result BLUE-PENCIL
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.