The most common and most likely answer to this crossword clue is the 7 letter word ASHAMED
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result ASHAMED
- Remorseful American hiding in an outhouse
- Embarrassed because pressman eats meat
- Embarrassed because news boss engages amateur
- Sorry there’s no proper leader for the paper
- Embarrassed when theatrical person meets newsman
- Embarrassed when bad actor heads to exit drunk
- Cinders made trouble and is sorry
- A phoney party leader being sheepish?
- A bogus journalist wishing he hadn’t done it?
- A bogus journalist getting red-faced
Buddy explains!

The straight part
We know that "feeling embarrassed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case feeling embarrassed = ashamed.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 ASHAMED mean?
ASHAMED verb- To feel shame; to be ashamed.
- To make ashamed; to shame.
- Feeling shame or guilt.