The most common and most likely answer to this crossword clue is the 7 letter word STROPHE
I've seen this crossword clue in The Daily Telegraph
S
T
R
O
P
H
E
More clues leading to the result STROPHE
- Burst of anger at explosive piece of verse
- Chap following wobbly lines
- Bit of choral singing Hot Press briefly hammered
- Greek song others performed around piano
- Paddy, Henry and Earl produce choral movement
- What makes keen fellow produce part of poem?
- Bad temper the fellow’s revealed in Greek song
- Choral song before explosive fit of temper
- He’s keen to introduce part of lyric poem
- The prose mostly inappropriate? Bit of poetry called for
Buddy explains!

The straight part
We know that "Greek song" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case greek song = strophe.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 STROPHE mean?
STROPHE noun- A turn in verse, as from one metrical foot to another, or from one side of a chorus to the other.
- The section of an ode that the chorus chants as it moves from right to left across the stage.
- A pair of stanzas of alternating form on which the structure of a given poem is based.