The most common and most likely answer to this crossword clue is the 11 letter word LUCUBRATION
I've seen this crossword clue in The Times
L
U
C
U
B
R
A
T
I
O
N
Buddy explains!

The straight part
We know that "Late study" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case late study = lucubration.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.
Crossword Answer definitions
LUCUBRATION noun- Intense and prolonged study or meditation; especially, late at night.
- The product of such study; often, writings.