There's no airs, oddly, in looking smart (5)
I believe the answer is:
sting
'smart' is the definition.
(both can mean to burn or hurt)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for sting that I've seen before include "Goad" , "English musician, b. 1951 -- a sudden pain" , "Entrapment operation; sharp pain" , "Smart - swindle" , "Bee's weapon" .)