Cryptic crossword clue
States accepted by worn-out horses having these on their backs 10

The most common and most likely answer to this crossword clue is the 10 letter word HAVERSACKS

I've seen this crossword clue in The Daily Telegraph
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Buddy explains!

The straight part
We know that "these on their backs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case these on their backs = haversacks.
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 HAVERSACKS mean?

HAVERSACKS noun
  1. A small, strong bag carried on the back or the shoulder, usually with only one strap, and originally made of canvas.
  2. An oat-sack, or nosebag for a horse.

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