The most common and most likely answer to this crossword clue is the 8 plus 5 letter word PEMBROKE TABLE
I've seen this crossword clue in Financial Times
P
E
M
B
R
O
K
E
T
A
B
L
E
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 = pembroke table.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.