The shooting of some mosquitoes, we’re told (5)
I believe the answer is:
Here is my best explanation:
'the shooting' is the definition.
(skeet is a kind of shooting)
I can't explain the remainder of the clue.
(Other definitions for skeet that I've seen before include "A form of clay-pigeon shooting", "American clay pigeon shooting", "Form of clay pigeon shooting", "Sport involving clay pigeons" and "US version of a shooting sport involving clay pigeons".)