The most common and most likely answer to this crossword clue is the 6 plus 5 letter word BANANA SKINS
I've seen this crossword clue in The Guardian
B
A
N
A
N
A
S
K
I
N
S
Buddy explains!
The straight part
We know that "cause for embarrassment? They’re out of hand" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cause for embarrassment? they’re out of hand = banana skins.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.