The most common and most likely answer to this crossword clue is the 10 letter word ENTREATING
I've seen this crossword clue in The Guardian
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Buddy explains!
The straight part
We know that "Begging" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case begging = entreating.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 ENTREATING mean?
ENTREATING verb- To treat with, or in respect to, a thing desired; hence, to ask for earnestly.
- To beseech or supplicate (a person); to prevail upon by prayer or solicitation; to try to persuade.
- To invite; to entertain.
- To treat or discourse; hence, to enter into negotiations, as for a treaty.
- To make an earnest petition or request.
- To treat, or conduct toward; to deal with; to use.
- Entreaty