Cat, say - maybe a cat - no, a dog (7)
I believe the answer is:
whippet
'a dog' is the definition.
(I know that Whippet is a type of greyhound)
'cat say maybe a cat no' is the wordplay.
I cannot really see how this works, but
'cat' could be 'whip' (cat o' nine tails or cat is a type of whip) and 'whip' is located in the answer.
'a cat' could be 'pet' (cat is an example of a pet) and 'pet' is found in the answer.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for whippet that I've seen before include "racing animal" , "Dog bred for racing" , "Small greyhound-type dog" , "Small slender breed of dog like a greyhound" , "Dog related to 9 down" .)