Hurried to include a song that's turned out (7)
I believe the answer is:
splayed
'turned out' is the definition.
('splay' can be a synonym of 'turn out')
'hurried to include a song' is the wordplay.
'hurried' becomes 'sped' ('speed' can be a synonym of 'hurry').
'to include' indicates putting letters inside.
'a song' becomes 'lay' (poetic term for a song).
'sped' enclosing 'lay' is 'SPLAYED'.
'that's' acts as a link.
(Other definitions for splayed that I've seen before include "with legs apart" , "Spread apart" , "Turned out" .)