The most common and most likely answer to this crossword clue is the 6 letter word INFULA
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The straight part
We know that "Appendage to mitre" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case appendage to mitre = infula.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 INFULA mean?
INFULA noun- A fillet of white wool, worn on the head by ancient Roman priests
- A head covering worn by early Christian priests
- A ribbon on a bishop's mitre