Flyer in green place for running (9,6)
I believe the answer is:
peregrine falcon
'flyer' is the definition.
(type of bird)
'in green place for running' is the wordplay.
'running' indicates anagramming the letters (the letters run around to different places).
'in'+'green'+'place'+'for'='ingreenplacefor'
'ingreenplacefor' with letters rearranged gives 'PEREGRINE FALCON'.
(Other definitions for peregrine falcon that I've seen before include "She kills small creatures" , "bird?" , "up in the air?" .)