Cryptic crossword clue
Highly desirable Greek character – tonsor, initially – to remove hair outside 4-4

The most common and most likely answer to this crossword clue is the 9 letter word MUST-HAVE

I've seen this crossword clue in Financial Times
M
U
S
T
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H
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Buddy explains!

The straight part
We know that "Highly desirable" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case highly desirable = must-have.
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 MUST-HAVE mean?

MUST-HAVE noun
  1. An item that one must own, or a feature that is essential to a service, etc.
MUST-HAVE adjective
  1. Essential to own.

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