The most common and most likely answer to this crossword clue is the 7 letter word WITHERS
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Buddy explains!
The straight part
We know that "Part of horse/shrinks" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of horse/shrinks = withers.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 WITHERS mean?
WITHERS verb- To shrivel, droop or dry up, especially from lack of water.
- To cause to shrivel or dry up.
- To lose vigour or power; to languish; to pass away.
- To become helpless due to emotion.
- To make helpless due to emotion.
- To go against, resist; oppose.
- The part of the back of a four-legged animal that is between the shoulder blades; in many species the highest point of the body and the standard place to measure the animal's height.