The most common and most likely answer to this crossword clue is the 5 letter word PANNE
P
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N
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The straight part
We know that "have a significant nap" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case have a significant nap = panne.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 PANNE mean?
PANNE noun- A lustrous finish applied to velvet and satin.
- A fabric resembling velvet, but having the nap flat and less close.
- A wetland consisting of a small depression, with or without standing water, often in a salt marsh or other coastal wetland.