The most common and most likely answer to this crossword clue is the 4 plus 4 letter word PEER GYNT
I've seen this crossword clue in Financial Times
P
E
E
R
G
Y
N
T
More clues leading to the result PEER GYNT
- Shut up about unusually grey play by Ibsen
- Play part with inner energy note to the end
- Drama when a republican expelled from Green Party organisation
- A guy less content with books about English drama
- Marie leaves prayer-meeting confused about Grieg’s incidental music
- Suites arranged to suit Norwegian’s booking?
- Shut up about grey novel that was written by Ibsen
- Force to drop name in part for play
- Play part storing renewable energy?
- Drama in gym — gentry involved
Buddy explains!

The straight part
We know that "Grieg’s incidental music" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case grieg’s incidental music = peer gynt.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.