The most common and most likely answer to this crossword clue is the 6 plus 8 letter word ENFANT TERRIBLE
I've seen this crossword clue in The Daily Telegraph
E
N
F
A
N
T
T
E
R
R
I
B
L
E
More clues leading to the result ENFANT TERRIBLE
- Provocative example of issue produced in Paris?
- Doctor Bear felt intern to be a brat
- Embarrassingly ghastly French kid?
- Ref let banter in game become subject of controversy?
- A growing problem for Maman et Papa?
- Relent with brat? Fine. Unfortunately this could be the outcome
- Unruly infernal teen brat yielding a name — this?
- Better to break with infernal nonconformist
- Embarrassing type‘s issue in France?
- Relent if banter upset, embarrassing non-conformist
Buddy explains!
The straight part
We know that "Embarrassing person" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case embarrassing person = enfant terrible.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.