The most common and most likely answer to this crossword clue is the 6 letter word BOUNCE
I've seen this crossword clue in The Guardian
B
O
U
N
C
E
More clues leading to the result BOUNCE
Buddy explains!

The straight part
We know that "Exuberance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case exuberance = bounce.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 BOUNCE mean?
BOUNCE noun- A change of direction of motion after hitting the ground or an obstacle.
- A movement up and then down (or vice versa), once or repeatedly.
- An email return with any error.
- The sack, licensing.
- A bang, boom.
- A drink based on brandyW.
- A heavy, sudden, and often noisy, blow or thump.
- Bluster; brag; untruthful boasting; audacious exaggeration; an impudent lie; a bouncer.
- Scyliorhinus canicula, a European dogfish.
- A genre of New Orleans music.
- Drugs.
- Swagger.
- A 'good' beat.
- A talent for leaping.
- To change the direction of motion after hitting an obstacle.
- To move quickly up and then down, or vice versa, once or repeatedly.
- To cause to move quickly up and down, or back and forth, once or repeatedly.
- To suggest or introduce (an idea, etc.) to (off or by) somebody, in order to gain feedback.
- To leap or spring suddenly or unceremoniously; to bound.
- To move rapidly (between).
- (of a cheque/check) To be refused by a bank because it is drawn on insufficient funds.
- To fail to cover (have sufficient funds for) (a draft presented against one's account).
- To leave.
- To eject violently, as from a room; to discharge unceremoniously, as from employment.
- (sometimes employing the preposition with) To have sexual intercourse.
- (air combat) To attack unexpectedly.
- To turn power off and back on; to reset
- (of an e-mail message or address) To return undelivered.
- To land hard and lift off again due to excess momentum.
- (skydiving) To land hard at unsurvivable velocity with fatal results.
- (sound recording) To mix (two or more tracks of a multi-track audio tape recording) and record the result onto a single track, in order to free up tracks for further material to be added.
- To bully; to scold.
- To strike or thump, so as to rebound, or to make a sudden noise; to knock loudly.
- To boast; to bluster.