Shortly aiming for painkiller (7)
I believe the answer is:
aspirin
'for painkiller' is the definition.
(aspirin is a kind of painkiller)
'shortly aiming' is the wordplay.
'shortly' means to remove the last letter.
'aiming' becomes 'aspiring' ('aspire' can be a synonym of 'aim').
'aspiring' with its last letter taken away is 'ASPIRIN'.
(Other definitions for aspirin that I've seen before include "Synthetic analgesic" , "Analgesic over in Paris" , "Analgesic compound" , "Headache killer?" , "Common analgesic drug" .)