Equally big name in charge, leading a country (5,4)
I believe the answer is:
costa rica
'country' is the definition.
(Costa Rica is an example)
'equally big name in charge leading a' is the wordplay.
'equally big name' becomes 'costar' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'in charge' becomes 'ic' (abbreviation for 'in charge').
'leading' means one lot of letters go next to another.
'costar'+'ic'+'a'='COSTA RICA'
Can you help me to learn more?
(Other definitions for costa rica that I've seen before include "A Socratic country in Central America, oddly" , "Central American state" , "source of coffee" , "Central American republic" , "Central American nation" .)