The most common and most likely answer to this crossword clue is the 5 plus 5 letter word CARGO PANTS
C
A
R
G
O
P
A
N
T
S
More clues leading to the result CARGO PANTS
Buddy explains!
The straight part
We know that "piece of costume" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case piece of costume = cargo pants.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.