Country type agitated about end of hunting (5)
I believe the answer is:
egypt
'country' is the definition.
(Egypt is an example)
'type agitated about end of hunting' is the wordplay.
'agitated' is an anagram indicator.
'about' is an insertion indicator.
'end of' suggests the final letters.
The final letter of 'hunting' is 'g'.
'type' is an anagram of 'eypt'.
'eypt' going around 'g' is 'EGYPT'.
(Other definitions for egypt that I've seen before include "NE African country" , "North African nation" , "Cleopatra its queen" , "Sudan, Israel neighbour" , "N. African country" .)