The most common and most likely answer to this crossword clue is the 6 plus 3 plus 4 letter word LITTLE BOY BLUE
I've seen this crossword clue in The Times
L
I
T
T
L
E
B
O
Y
B
L
U
E
Buddy explains!
The straight part
We know that "nursery rhyme" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nursery rhyme = little boy blue.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.