The most common and most likely answer to this crossword clue is the 11 letter word APPROPRIATE
I've seen this crossword clue in The Guardian
A
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More clues leading to the result APPROPRIATE
Buddy explains!

The straight part
We know that "double defn." is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case double defn. = appropriate.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 APPROPRIATE mean?
APPROPRIATE verb- To make suitable; to suit.
- To take to oneself; to claim or use, especially as by an exclusive right.
- To set apart for, or assign to, a particular person or use, especially in exclusion of all others; with to or for.
- To annex (for example a benefice, to a spiritual corporation, as its property).
- Suitable or fit; proper.
- Suitable to the social situation or to social respect or social discreetness; socially correct; socially discreet; well-mannered; proper.
- Set apart for a particular use or person; reserved.