An artist going round King Arthur's first capital (6)
I believe the answer is:
ankara
'capital' is the definition.
(capital of Turkey)
'an artist going round king arthur's first' is the wordplay.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'going round' means one lot of letters goes inside another (some letters go around others).
'king' becomes 'K' (abbreviation for king in chess).
'arthur's first' becomes 'a' (1st letter of 'arthur').
'an'+'ra'='anra'
'k'+'a'='ka'
'anra' enclosing 'ka' is 'ANKARA'.
(Other definitions for ankara that I've seen before include "Capital of 8 across" , "European capital" , "Capital of Turkey" , "Turkish capital" , "Capital established by Ataturk" .)