The most common and most likely answer to this crossword clue is the 12 letter word SHEEPISHNESS
I've seen this crossword clue in The Daily Telegraph
S
H
E
E
P
I
S
H
N
E
S
S
Buddy explains!
The straight part
We know that "an embarrassed one" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an embarrassed one = sheepishness.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.