Cartoon dog (6)
'cartoon dog' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for snoopy that I've seen before include "Prying - cartoon dog" , "Brown dog's" , "Curious" , "Charlie Brown's cartoon dog" , "Charlie Brown's canine companion" .)
(Another definition for astro that I've seen is " Indicates a heavenly body".)