Cryptic crossword clue
Orderly arrangement: finished one accepted by admired personage 9

The most common and most likely answer to this crossword clue is the 9 letter word LINEATION

L
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Buddy explains!

The straight part
We know that "Orderly arrangement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case orderly arrangement = lineation.
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 LINEATION mean?

LINEATION noun
  1. A linear feature in rock, often structural
  2. The way in which line breaks are inserted in a poem

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