The most common and most likely answer to this crossword clue is the 5 plus 2 plus 7 letter word CHEST OF DRAWERS
I've seen this crossword clue in The Times
C
H
E
S
T
O
F
D
R
A
W
E
R
S
More clues leading to the result CHEST OF DRAWERS
- Dearth of screws spoiled clothing unit
- Gent almost picked up prize in game – a piece of furniture
- Dresser for the bosom of artists?
- Bureau concerned with bloomers: briefs collected here
- Part of bedroom set from Knickerbox
- Freshwater cod’s not usually found in this storage facility
- Piece of furniture and part of trunk belonging to some artists
- Artists’ bust piece of furniture?
- Game about to end in grief with prize going back in storage unit
Buddy explains!

The straight part
We know that "clothing unit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case clothing unit = chest of drawers.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.