The most common and most likely answer to this crossword clue is the 5 letter word ESSAY
I've seen this crossword clue in Financial Times
E
S
S
A
Y
More clues leading to the result ESSAY
- Composition — first of Elgar’s symphonies, for example
- Fool around with looker briefly outside bash?
- Try to produce written work for tutor?
- Study art in Paris, perhaps
- Composition in Monet's art, for example
- Composition of French art, for example
- Try South Africa, as briefly suggested
- Attempt to speak in support of drugs
- Tract from English Society for example
- Try Mensa, oddly getting rejected, perhaps
Buddy explains!

The straight part
We know that "Paper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case paper = essay.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 ESSAY mean?
ESSAY noun- (authorship) A written composition of moderate length, exploring a particular issue or subject.
- A test, experiment; an assay.
- An attempt.
- A proposed design for a postage stamp or a banknote.
- To try.
- To move forth, as into battle.