The most common and most likely answer to this crossword clue is the 6 letter word BALDER
I've seen this crossword clue in Independent
B
A
L
D
E
R
Buddy explains!

The straight part
We know that "thinning out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case thinning out = balder.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 BALDER mean?
BALDER adjective- Having no hair, fur or feathers.
- (by extension) Denuded of any hair- or fur-like covering.
- Of tyres: whose surface is worn away.
- (of a statement or account) Unembellished.
- (of a statement) Without evidence or support being provided.