The most common and most likely answer to this crossword clue is the 4 plus 3 plus 4 letter word JACK AND JILL
J
A
C
K
A
N
D
J
I
L
L
More clues leading to the result JACK AND JILL
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 = jack and jill.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.