The most common and most likely answer to this crossword clue is the 7 letter word TUMBRIL
I've seen this crossword clue in Financial Times
T
U
M
B
R
I
L
More clues leading to the result TUMBRIL
Buddy explains!

The straight part
We know that "cart" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cart = tumbril.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 TUMBRIL mean?
TUMBRIL noun- A kind of medieval torture device, later associated with a cucking stool.
- A cart which opens at the back to release its load.
- A cart used to carry condemned prisoners to their death, especially to the guillotine during the French Revolution.
- A basket or cage of osiers, willows, or the like, to hold hay and other food for sheep.