The most common and most likely answer to this crossword clue is the 10 letter word NARCOLEPSY
I've seen this crossword clue in The Guardian
N
A
R
C
O
L
E
P
S
Y
Buddy explains!
The straight part
We know that "sleeping sickness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sleeping sickness = narcolepsy.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 NARCOLEPSY mean?
NARCOLEPSY noun- A disorder characterized by sudden and uncontrollable attacks of deep sleep, often brief, sometimes accompanied by paralysis and hallucinations