The most common and most likely answer to this crossword clue is the 8 letter word BODYSUIT
I've seen this crossword clue in Financial Times
B
O
D
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T
Buddy explains!

The straight part
We know that "close-fitting garment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case close-fitting garment = bodysuit.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 BODYSUIT mean?
BODYSUIT noun- A one-piece, skin-tight garment rather like a leotard.