Country each artist urged regularly to visit (7)
I believe the answer is:
'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 "North-east African state", "Country in the Horn of Africa", "Northeast African country", "Asmara area", "State north of Ethiopia".)