The sport of shooting at flying 'saucers' (5)
I believe the answer is:
skeet
'the sport' is the definition.
(thesaurus)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for skeet that I've seen before include "Form of clay pigeon shooting" , "American clay pigeon shooting" , "A form of clay-pigeon shooting" , "US version of a shooting sport involving clay pigeons" .)