The most common and most likely answer to this crossword clue is the 7 plus 6 letter word INITIAL RHYMES
I
N
I
T
I
A
L
R
H
Y
M
E
S
Buddy explains!
The straight part
We know that "composed in alliterations" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case composed in alliterations = initial rhymes.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.