The most common and most likely answer to this crossword clue is the 6 letter word SHEESH
I've seen this crossword clue in The Times
S
H
E
E
S
H
Buddy explains!

The straight part
We know that "Exclamation of surprise" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case exclamation of surprise = sheesh.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 SHEESH mean?
SHEESH interjection- An expression of exasperation.