Old archbishop accepting record player, a thing for retirement (3,6)
I believe the answer is:
bed jacket
'thing for retirement' is the definition.
(something worn when retiring to bed)
'old archbishop accepting record player a' is the wordplay.
'old archbishop' becomes 'Becket' (Thomas Becket, Archbishop of Canterbury, 1162-1170).
'accepting' indicates putting letters inside (inserted letters are accepted).
'record player' becomes 'dj' (DJs play records).
'dj'+'a'='dja'
'becket' enclosing 'dja' is 'BED-JACKET'.
(Other definitions for bed jacket that I've seen before include "Item of night attire" , "Nightwear" .)