Playful writer’s found in record store (7)
I believe the answer is:
archive
'record store' is the definition.
(where records are stored)
'playful writer's' is the wordplay.
'playful' becomes 'arch' (I've seen this before).
'writer's' becomes 'i've' ('I have' can refer to the person writing).
'arch'+'ive'='ARCHIVE'
'found in' acts as a link.
(Other definitions for archive that I've seen before include "Document depository" , "File away" , "Depository containing historical records" , "Historical collection of documents" , "store for the future" .)