The most common and most likely answer to this crossword clue is the 2 plus 4 letter word MY WORD
I've seen this crossword clue in The Times
M
Y
W
O
R
D
Buddy explains!
The straight part
We know that "It is surprising/I promise to give this" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it is surprising/i promise to give this = my word.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.