Hit that pest! (4)
I believe the answer is:
slug
This clue is a double definition.
'hit' is the first definition.
(I know that slug is a more specific form of the action hit)
'pest' is the second definition.
(I've seen this before)
'that' acts as a link.
(Other definitions for slug that I've seen before include "Bullet; swig" , "Slimy pest" , "Shell-less mollusc ? bullet" , "slimy type" , "Small creature like snail without shell" .)