Country in Chad regularly chasing leading actor (5,4)
I believe the answer is:
costa rica
'country' is the definition.
(Costa Rica is an example)
'in chad regularly chasing leading actor' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'chasing' says to put letters next to each other (some letters chase after others).
'leading actor' becomes 'co-star' (eg one of the stars of a film).
'in'+'chad'='inchad'
The alternating letters of 'inchad' are 'ica'.
'ica' after 'costar' is 'COSTA RICA'.
(Other definitions for costa rica that I've seen before include "Central American republic" , "Central American country, capital San Jose" , "Central American state" , "Central American nation" , "place in Central America" .)