Small explosion a little after noon — drive off (7)
I believe the answer is:
atishoo
'small explosion' is the definition.
'atishoo' can be an answer for 'explosion' (representation of the sound of a sneeze). I am unsure of the 'small' bit.
'a little after noon drive off' is the wordplay.
'a little after noon' becomes 'ati' (I can't justify this - if you can you should believe this answer much more).
'drive off' becomes 'shoo' (shoo can mean to drive off or send away).
'ati'+'shoo'='ATISHOO'
Can you help me to learn more?
(Other definitions for atishoo that I've seen before include "Word to be sneezed at" , "Sound of a sneeze" , "Sound made on expiration" , "Sneezing sound" , "hay-fever sufferer may interject this" .)