Alien nursing severe pain in African state (5)
I believe the answer is:
egypt
'african state' is the definition.
(country in Africa)
'alien nursing severe pain' is the wordplay.
'alien' becomes 'et' (extraterrestrial).
'nursing' means one lot of letters goes inside another.
'severe pain' becomes 'gyp'.
'et' enclosing 'gyp' is 'EGYPT'.
'in' acts as a link.
(Other definitions for egypt that I've seen before include "Where M. Antony died" , "Where Cavafy wrote" , "Ancient nation on the Nile" , "North East African republic" , "North African state" .)