Endless longing for painkiller (7)
I believe the answer is:
aspirin
'painkiller' is the definition.
(I know that aspirin is a type of painkiller)
'endless longing' is the wordplay.
'endless' means to remove the last letter.
'longing' becomes 'aspiring' (aspiring to something means longing for it).
'aspiring' with its final letter taken off is 'ASPIRIN'.
'for' acts as a link.
(Other definitions for aspirin that I've seen before include "Commonly used pain-killer" , "Common pain tablet" , "Analgesic compound" , "Headache pill" , "Pain-relieving drug made in Paris" .)