The most common and most likely answer to this crossword clue is the 4 plus 3 letter word MAKE ONE
I've seen this crossword clue in The Times
M
A
K
E
O
N
E
More clues leading to the result MAKE ONE
Buddy explains!
The straight part
We know that "to cause somebody delight or embarrassment?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to cause somebody delight or embarrassment? = make one.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.