The most common and most likely answer to this crossword clue is the 10 letter word APOLOGISED
I've seen this crossword clue in The Daily Telegraph
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Buddy explains!
The straight part
We know that "Expressed regret" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case expressed regret = apologised.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 APOLOGISED mean?
APOLOGISED verb- (often followed by “for”) To make an apology or excuse; to acknowledge some fault or offense, with expression of regret for it, by way of amends
- To express regret that a certain event has occurred.
- To make an apologia or defense; to act as apologist.