One king after another getting a writer (6,4)
I believe the answer is:
edward lear
'a writer' is the definition.
(I know that Edward Lear was a nonsense poet)
'one king after another' is the wordplay.
'one king' becomes 'edward' (I've seen this before).
'after' means one lot of letters go next to another.
'another' becomes 'lear' (I can't explain this - if you can you should believe this answer much more).
'edward'+'lear'='EDWARD LEAR'
'getting' is the link.
Can you help me to learn more?
(Other definitions for edward lear that I've seen before include "Humorist" , "literary figure" , "Author" , "19th century nonsense poet" , "He painted birds" .)