The most common and most likely answer to this crossword clue is the 7 letter word DUDGEON
I've seen this crossword clue in The Times
D
U
D
G
E
O
N
More clues leading to the result DUDGEON
- Resentment once of failure, gone bad
- Failure has gone wrong, leading to pique
- Resentment of first couple in club going for date
- Useless dope taking over — resentment generally high
- When high, this causes intense indignation
- Resentment created by faulty information about love
- Dead fish not good, causing resentment
- Duke conceals first name in prison, creating indignation
- Offended indignation for failure? Gone bust!
- Person failing has gone off showing indignation
Buddy explains!

The straight part
We know that "pique" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pique = dudgeon.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 DUDGEON mean?
DUDGEON noun- A kind of wood used especially in the handles of knives; the root of the box tree.
- A hilt made of this wood.
- A dagger which has a dudgeon hilt.
- A feeling of anger or resentment.