The most common and most likely answer to this crossword clue is the 9 letter word ADVENTURE
I've seen this crossword clue in The Daily Telegraph
A
D
V
E
N
T
U
R
E
More clues leading to the result ADVENTURE
- Bill undertaking possibly hazardous trip
- Exciting time, coming by river
- Coming over a river, which may be exciting
- Exploit commercial opening on Northern river
- Risk these days putting outlet by river
- Coming to river — that may be exciting
- Coming by northern river for exciting experience
- Period in December not initially certain to provide exciting event
- Tavern due for renovation is a risky undertaking
- Risk Dixieland intro in rave tune remix
Buddy explains!

The straight part
We know that "that may be exciting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that may be exciting = adventure.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 ADVENTURE mean?
ADVENTURE noun- The encountering of risks; a bold undertaking, in which dangers are likely to be encountered, and the issue is staked upon unforeseen events; a daring feat.
- A remarkable occurrence; a striking event.
- A mercantile or speculative enterprise of hazard; a venture; a shipment by a merchant on his own account.
- A feeling of desire for new and exciting things.
- A text adventure or an adventure game.
- That which happens by chance; hazard; hap.
- Chance of danger or loss.
- Risk; danger; peril.
- To risk or hazard; jeopard; venture.
- To venture upon; to run the risk of; to dare.
- To try the chance; to take the risk.