The most common and most likely answer to this crossword clue is the 7 letter word TYMPANI
I've seen this crossword clue in The Daily Telegraph
T
Y
M
P
A
N
I
More clues leading to the result TYMPANI
Buddy explains!

The straight part
We know that "Source of the biggest hits of the Proms?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case source of the biggest hits of the proms? = tympani.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.
What does TYMPANI mean?
TYMPANI noun- The set of precision kettledrums in an orchestra.