The most common and most likely answer to this crossword clue is the 4 plus 3 plus 6 plus 2 plus 4 plus 4 letter word BURN THE CANDLE AT BOTH ENDS
I've seen this crossword clue in The Times
B
U
R
N
T
H
E
C
A
N
D
L
E
A
T
B
O
T
H
E
N
D
S
Buddy explains!
The straight part
We know that "to rest only a little" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to rest only a little = burn the candle at both ends.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.