The most common and most likely answer to this crossword clue is the 12 letter word ORGANISATION
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More clues leading to the result ORGANISATION
Buddy explains!

The straight part
We know that "Establishment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case establishment = organisation.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 ORGANISATION mean?
ORGANISATION noun- The quality of being organized.
- The way in which something is organized, such as a book or an article.
- A group of people or other legal entities with an explicit purpose and written rules.
- A group of people consciously cooperating.
- A major league club and all its farm teams.