Old way adopted by American writer in selling approach (4,5)
I believe the answer is:
mail order
'selling approach' is the definition.
(way of selling things)
'old way adopted by american writer' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'way' becomes 'rd' (short for road).
'adopted by' means one lot of letters goes inside another (I've seen this in other clues).
'american writer' becomes 'Mailer' (Norman Mailer, 1923-2007).
'o'+'rd'='ord'
'ord' put into 'mailer' is 'MAIL-ORDER'.
'in' is the link.
(Other definitions for mail order that I've seen before include "Way to shop" , "Type of purchase" , "type of catalogue" , "that one's sent for?" , "Means of shopping" .)