Cryptic crossword clue
Constant publicity about Dior’s last perfume 6

The most common and most likely answer to this crossword clue is the 6 letter word CHYPRE

I've seen this crossword clue in The Times
C
H
Y
P
R
E

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The straight part
We know that "perfume" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case perfume = chypre.
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 CHYPRE mean?

CHYPRE noun
  1. Any of a family of fragrances built on a base consisting of bergamot, oakmoss and labdanum.

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