Run south, back to get in the water for an insect killer (3,7)
I believe the answer is:
fly swatter
'an insect killer' is the definition.
The definition suggests a singular noun which matches the answer.
'run south back to get in the water' is the wordplay.
'run south back' becomes 'flys' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'to get in' is an insertion indicator (the word gets some letters inside).
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
't' placed into 'water' is 'watter'.
'flys'+'watter'='FLY-SWATTER'
'for' is the link.
Can you help me to learn more?
(Other definitions for fly swatter that I've seen before include "For insect repeller" , "Insect killing device" .)