Country each artist urged regularly to visit (7)
'country' is the definition.
(I've seen this before)
'each artist urged regularly to visit' is the wordplay.
'each' becomes 'ea'.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'to visit' indicates putting letters inside.
The alternating letters of 'artisturged' are 'ritre'.
'ea' placed around 'ritre' is 'ERITREA'.
(Other definitions for eritrea that I've seen before include "It achieved independence from Ethiopia in 1993", "It became independent of Ethiopia in 1993", "Northeast African country", "Province of Ethiopia on the Red Sea", "North-east African state".)