The most common and most likely answer to this crossword clue is the 10 letter word WRAPAROUND
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result WRAPAROUND
Buddy explains!

The straight part
We know that "this garment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case this garment = wraparound.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 WRAPAROUND mean?
WRAPAROUND noun- A garment that is wrapped around the body and tied.
- A label or advertising display that wraps around a container.
- A segment where material featuring one person (such as a reporter) is introduced and concluded by another person.
- An extension to a property that combines side and rear extensions.
- Word wrap, the word processing feature that moves text on to the next line if it will not fit on the current one.
- Wrapping of numerical value in case of underflow or overflow
- (of clothing) designed to be wrapped around the body and tied
- (of windows, lenses, etc.) that extends around a corner or bend
- Serving to surround or bookend something else.
- A form of mortgage in which the seller of a property extends to the buyer a junior mortgage which exists in addition to any superior mortgages already secured on the property. The seller accepts a secured promissory note from the buyer for the amount due on the underlying mortgage plus an amount up to the remaining purchase-money balance.