The most common and most likely answer to this crossword clue is the 6 letter word YEEHAW
I've seen this crossword clue in The Times
Y
E
E
H
A
W
Buddy explains!

The straight part
We know that "shout at rodeos" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shout at rodeos = yeehaw.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 YEEHAW mean?
YEEHAW verb- To shout yee-haw, or to otherwise exclaim in a similar manner.
- An expression of joy or excitement, commonly associated with cowboys.