The most common and most likely answer to this crossword clue is the 8 letter word JUBILANT
I've seen this crossword clue in The Times
J
U
B
I
L
A
N
T
More clues leading to the result JUBILANT
- Man’s ending in jail, but strangely very happy
- In transport project, including most of big network
- Rejoicing in lab crazily interrupts project
- Transported con’s last in jail but being reformed
- Over the moon — until jab goes wrong
- Joyful short jaunt around Bali with new Tesla
- Number thrown into jail, but strangely happy
- Rejoicing until jab is thrown
Buddy explains!

The straight part
We know that "Rejoicing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rejoicing = jubilant.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 JUBILANT mean?
JUBILANT adjective- In a state of elation.