The most common and most likely answer to this crossword clue is the 1 plus 3 letter word I SAY
I've seen this crossword clue in The Times
I
S
A
Y
More clues leading to the result I SAY
- One's always producing surprised exclamation
- My investment company's base
- One share in decision that's a surprise
- “WTF” clip from Alexei Sayle
- Attractive option for those saving yen? Get that!
- My word is annoying you at first
- Goodness regularly seen in Miss Mary?
- A twist of celery as inherent goodness!
- Given the odds, it’s easy for old Gordon Bennett!
- “Gosh!” = “ok”
Buddy explains!

The straight part
We know that "that's a surprise" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that's a surprise = i say.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.