The most common and most likely answer to this crossword clue is the 9 letter word BUCKBOARD
I've seen this crossword clue in The Guardian
B
U
C
K
B
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A
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D
Buddy explains!
The straight part
We know that "Simple carriage" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case simple carriage = buckboard.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 BUCKBOARD mean?
BUCKBOARD noun- A simple, distinctively American four-wheeled horse-drawn wagon designed for personal transport as well as for transporting animal fodder and domestic goods, often with a spring-mounted seat for the driver.