The most common and most likely answer to this crossword clue is the 9 letter word CLIPBOARD
I've seen this crossword clue in The Daily Telegraph
C
L
I
P
B
O
A
R
D
Buddy explains!
The straight part
We know that "backing for paper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case backing for paper = clipboard.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 CLIPBOARD mean?
CLIPBOARD noun- A flat piece of rigid material, such as card or plastic, with a clip at one end under which papers can be held.
- A buffer in memory where the user can store data temporarily while transferring it from one place within an application to another or between applications.