The most common and most likely answer to this crossword clue is the 4 plus 6 letter word FOAM RUBBER
I've seen this crossword clue in Independent
F
O
A
M
R
U
B
B
E
R
More clues leading to the result FOAM RUBBER
Buddy explains!

The straight part
We know that "Element of upholstery" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case element of upholstery = foam rubber.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.