The most common and most likely answer to this crossword clue is the 11 letter word YELLOWSTONE
I've seen this crossword clue in The Times
Y
E
L
L
O
W
S
T
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N
E
More clues leading to the result YELLOWSTONE
- River Tees only low after diversion
- US river where chicken put to death
- The most timid avoid eastern unit in national park
- Chicken satay and tikka starters at lunchtime, current in the western US
- Zircon, say, found in American park?
- Some US cabs are painted so, notes vagrant, park there
- Chicken on a rock in the park
Buddy explains!

The straight part
We know that "US river" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case us river = yellowstone.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.