The most common and most likely answer to this crossword clue is the 10 letter word PERIWIGGED
I've seen this crossword clue in Financial Times
P
E
R
I
W
I
G
G
E
D
Buddy explains!
The straight part
We know that "wearing a hairpiece" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wearing a hairpiece = periwigged.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.