The most common and most likely answer to this crossword clue is the 7 letter word SHAMING
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Buddy explains!

The straight part
We know that "Embarrassing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case embarrassing = shaming.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 SHAMING mean?
SHAMING verb- To cause to feel shame.
- To cover with reproach or ignominy; to dishonor; to disgrace.
- To drive or compel by shame.
- To feel shame, be ashamed.
- To mock at; to deride.
- The activity by which somebody is shamed.