The most common and most likely answer to this crossword clue is the 4 plus 9 letter word TIME SIGNATURE
T
I
M
E
S
I
G
N
A
T
U
R
E
Buddy explains!
The straight part
We know that "indication of rhythm" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case indication of rhythm = time signature.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.