The most common and most likely answer to this crossword clue is the 7 letter word BRITPOP
I've seen this crossword clue in The Times
B
R
I
T
P
O
P
Buddy explains!
The straight part
We know that "music of the 1990s" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case music of the 1990s = britpop.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.