The most common and most likely answer to this crossword clue is the 7 letter word PELISSE
P
E
L
I
S
S
E
More clues leading to the result PELISSE
Buddy explains!

The straight part
We know that "Furry garment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case furry garment = pelisse.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 PELISSE mean?
PELISSE noun- A fur-lined or fur robe or gown, especially as part of a uniform.
- A silk gown formerly worn by women, often lined or trimmed with fur.
- An overgarment worn by Victorian children when outside.