Note old symbol (4)
I believe the answer is:
logo
'symbol' is the definition.
(logo is a kind of symbol)
'note old' is the wordplay.
'note' becomes 'log' ().
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'log'+'o'='LOGO'
(Other definitions for logo that I've seen before include "A firm's sign or symbol" , "Printed symbol as emblem of organisation" , "Vigour; relish" , "Small emblem or device" , "Symbol or emblem used by organisation" .)