The most common and most likely answer to this crossword clue is the 11 letter word RESPECTABLY
I've seen this crossword clue in The Daily Telegraph
R
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S
P
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A
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Buddy explains!
The straight part
We know that "in a socially accepted manner" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in a socially accepted manner = respectably.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 RESPECTABLY mean?
RESPECTABLY adverb- In a respectable manner; so as to gain respect.
- Moderately; pretty well.