Their leaves flutter in the slightest breeze (6)
I believe the answer is:
aspens
'their leaves flutter in the slightest breeze' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for aspens that I've seen before include "Quivering poplars" , "Trembling poplars" , "Trees that shiver, kind of poplars" , "Trees with leaves that quiver" , "Species of poplars with leaves that quiver" .)