The most common and most likely answer to this crossword clue is the 8 letter word MONTEITH
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The straight part
We know that "old handkerchief" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old handkerchief = monteith.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 MONTEITH mean?
MONTEITH noun- A bowl used for the cooling or washing of wine glasses.
- A large 18th-century punchbowl, usually of silver, fluted and scalloped.
- A cotton handkerchief with white spots on a coloured background.