Country got hospital and new area, first of all (5)
I believe the answer is:
ghana
'country' is the definition.
(Ghana is an example)
'got hospital and new area first of all' is the wordplay.
'first of all' says to take the initial letters.
The first letters of 'got hospital and new area' is 'GHANA'.
(Other definitions for ghana that I've seen before include "Its capital is Accra" , "nation" , "Ah, nag one into going to Africa" , "West African country, independent since 1957" , "part of Africa" .)