Old Irish king and bishop relaxed in arbour (5,4)
I believe the answer is:
brian boru
'old irish king' is the definition.
(10th-century king)
'bishop relaxed in arbour' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'relaxed' is an anagram indicator.
'in'+'arbour'='inarbour'
'inarbour' with letters rearranged gives 'rianboru'.
'b'+'rianboru'='BRIAN BORU'
'and' acts as a link.
(Other definitions for brian boru that I've seen before include "King killed by Danes at the Battle of Clontarf" , "Irish king killed at the battle of Contarf" .)