Country starts to impose crippling austerity after Castro's broadcast (5,4)
I believe the answer is:
costa rica
'country' is the definition.
(Costa Rica is an example)
'starts to impose crippling austerity after castro's broadcast' is the wordplay.
'starts to' indicates taking the first letters.
'after' says to put letters next to each other.
'broadcast' indicates an anagram.
The initial letters of 'impose crippling austerity' is 'ica'.
'castro' anagrammed gives 'costar'.
'ica' put after 'costar' is 'COSTA RICA'.
(Other definitions for costa rica that I've seen before include "Central American state" , "source of coffee" , "A Socratic country in Central America, oddly" , "Central American republic" , "place in Central America" .)