The most common and most likely answer to this crossword clue is the 9 letter word HEADBOARD
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More clues leading to the result HEADBOARD
Buddy explains!

The straight part
We know that "part of the furniture" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of the furniture = headboard.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 HEADBOARD mean?
HEADBOARD noun- A vertical panel, either plain or upholstered, attached to the head of a bed.
- A panel, usually of metal, attached to the head of a fore-and-aft sail for additional strength.
- A board on the front of a train, carrying the train's name or that of the service it is on.
- A grave marker made of wood.