Spooner's dry grass, territory that would do for dog (9)
I believe the answer is:
greyhound
'dog' is the definition.
(greyhound is a kind of dog)
I don't understand the remainder of the clue.
(Other definitions for greyhound that I've seen before include "Speedy dog" , "Swift breed of dog" , "Fast-moving dog" , "Want to bet on it?" , "slender runner?" .)