The most common and most likely answer to this crossword clue is the 6 letter word PLUMMY
I've seen this crossword clue in The Daily Telegraph
P
L
U
M
M
Y
More clues leading to the result PLUMMY
Buddy explains!

The straight part
We know that "that’s surprising" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s surprising = plummy.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 PLUMMY mean?
PLUMMY adjective- Of, pertaining to, containing, or characteristic of plums
- Desirable; profitable; advantageous
- (of a voice) rich, mellow and carefully articulated, especially with an upper-class accent