The most common and most likely answer to this crossword clue is the 7 letter word KLEENEX
I've seen this crossword clue in The Guardian
K
L
E
E
N
E
X
More clues leading to the result KLEENEX
Buddy explains!
The straight part
We know that "an absorbing paper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an absorbing paper = kleenex.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 KLEENEX mean?
KLEENEX noun- A disposable tissue.