The most common and most likely answer to this crossword clue is the 6 letter word CRYPTO
I've seen this crossword clue in The Times
C
R
Y
P
T
O
Buddy explains!

The straight part
We know that "Secret" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case secret = crypto.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 CRYPTO mean?
CRYPTO noun- A secret supporter or follower.
- Cryptography.
- Cryptocurrency.
- Cryptococcus.
- Cryptosporidiosis.
- Secret or covert