The most common and most likely answer to this crossword clue is the 4 plus 3 plus 2 plus 6 letter word EYES OUT ON STALKS
I've seen this crossword clue in The Guardian
E
Y
E
S
O
U
T
O
N
S
T
A
L
K
S
Buddy explains!
The straight part
We know that "Looking surprised" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case looking surprised = eyes out on stalks.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.