The most common and most likely answer to this crossword clue is the 10 letter word SISTERHOOD
I've seen this crossword clue in The Guardian
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More clues leading to the result SISTERHOOD
Buddy explains!

The straight part
We know that "religious order" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case religious order = sisterhood.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 SISTERHOOD mean?
SISTERHOOD noun- The state, or kinship of being sisters
- The quality of being sisterly; sisterly companionship; especially, the sense that women have of being in solidarity with one another.
- A religious society of women
- The idea of universal experience amongst women, regardless of other traits or factors. (Considered obsolete in third-wave feminism.)