The most common and most likely answer to this crossword clue is the 6 letter word PEPLOS
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The straight part
We know that "old-fashioned robe" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old-fashioned robe = peplos.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 PEPLOS mean?
PEPLOS noun- An Ancient Greek garment, worn by women, formed of a tubular piece of cloth, which is folded back upon itself halfway down, until the top of the tube is worn around the waist, and the bottom covers the legs down to the ankles; the open top is then worn over the shoulders, and draped, in folds, down to the waist.