Record with old identifying symbol (4)
I believe the answer is:
logo
'symbol' is the definition.
(logo is a kind of symbol)
'record with old' is the wordplay.
'record' becomes 'log' (logging is a kind of recording).
'with' is a charade indicator (letters next to each other).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'log'+'o'='LOGO'
'identifying' is the link.
(Other definitions for logo that I've seen before include "Company emblem or device" , "Small design used as a company emblem" , "A company's printed symbol or emblem" , "Emblem, trade-mark" , "Printed symbol as emblem of organisation" .)