Way English archdeacon’s supported by Scottish writer (9)
I believe the answer is:
stevenson
'scottish writer' is the definition.
(Robert Louis Stevenson)
'way english archdeacon's supported by' is the wordplay.
'way' becomes 'st'.
'english' becomes 'e' (abbreviation).
'archdeacon's' becomes 'vens'.
'supported by' becomes 'on'.
'st'+'e'+'vens'+'on'='STEVENSON'
(Other definitions for stevenson that I've seen before include "Scottish writer" , "R L -, Kidnapped author" , "Robert Louis --, Scottish novelist" , "story-teller" , "Writer of Treasure Island, d. 1894" .)