Old king's unwell, onset of angina (4)
I believe the answer is:
offa
'old king's' is the definition.
(King of Mercia)
'unwell onset of angina' is the wordplay.
'unwell' becomes 'off' (as in feeling off).
'onset of' says to take the initial letters.
The initial letter of 'angina' is 'a'.
'off'+'a'='OFFA'
(Other definitions for offa that I've seen before include "King of Mercia, who may have built a dyke" , "Old Mercia king" , "One-time ruler" , "man throwing up defence" , "Mercian king, built dyke" .)