Awkwardly sway left, avoiding tip of huge pest killer (3,4)
I believe the answer is:
fly swat
'avoiding tip of huge pest killer' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.
'awkwardly sway left' is the wordplay.
I cannot quite see how this works, but
an anagram of 'sway' is 'yswa' which is within the answer.
'left' could be 'l' (common abbreviation) and 'l' is present in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Another definition for fly swat that I've seen is " Destroyer".)