The most common and most likely answer to this crossword clue is the 6 letter word SECRET
I've seen this crossword clue in The Times
S
E
C
R
E
T
More clues leading to the result SECRET
- Use Crete as setting for mystery
- Confidence in both dry and wet
- Morning service put back after Saint hushed prayer
- Private PA misses a line
- City about to block street, leaving no space between 3 and 12
- Undercover soldiers to infiltrate extremist group
- Clandestine faction assimilates religious teaching
- Small island, close to front, private
- Unknown Southern Greek island’s last to come to the fore
- Private clubs hidden in trees, oddly
Buddy explains!

The straight part
We know that "Confidence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case confidence = secret.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 SECRET mean?
SECRET noun- A piece of knowledge that is hidden and intended to be kept hidden.
- The key or principle by which something is made clear; the knack.
- Something not understood or known.
- Private seclusion.
- (in the plural) The genital organs.
- A form of steel skullcap.
- (often in the plural) Any prayer spoken inaudibly and not aloud; especially, one of the prayers in the Mass, immediately following the "orate, fratres", said inaudibly by the celebrant.
- To make or keep secret.
- To hide secretly.
- Being or kept hidden.
- Withdrawn from general intercourse or notice; in retirement or secrecy; secluded.
- Faithful to a secret; not inclined to divulge or betray confidence; secretive, separate, apart.
- Separate; distinct.