The most common and most likely answer to this crossword clue is the 9 letter word ATROPHIES
I've seen this crossword clue in The Guardian
A
T
R
O
P
H
I
E
S
More clues leading to the result ATROPHIES
Buddy explains!

The straight part
We know that "shrinks" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shrinks = atrophies.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 ATROPHIES mean?
ATROPHIES noun- A reduction in the functionality of an organ caused by disease, injury or lack of use.