Scottish writer holding vespers briefly on street (9)
I believe the answer is:
stevenson
'scottish writer' is the definition.
(Robert Louis Stevenson)
'vespers briefly on street' is the wordplay.
'vespers' becomes 'evensong' (similar church services).
'briefly' means to remove the last letter.
'on' means one lot of letters go next to another.
'street' becomes 'st'.
'evensong' with its last letter taken off is 'evenson'.
'evenson' after 'st' is 'STEVENSON'.
'holding' is the link.
(Other definitions for stevenson that I've seen before include "story-teller" , "Robert Louis -, Scots novelist" , "R L -, Kidnapped author" , "Writer of Treasure Island, d. 1894" , "Scottish writer" .)