The most common and most likely answer to this crossword clue is the 9 letter word TEREBINTH
T
E
R
E
B
I
N
T
H
Buddy explains!
The straight part
We know that "What you can get thinner from" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what you can get thinner from = terebinth.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 TEREBINTH mean?
TEREBINTH noun- A Mediterranean tree, Pistacia terebinthus (and, possibly, Pistacia palaestina)