The identifying sign of a record circle (4)
I believe the answer is:
logo
'the identifying sign' is the definition.
'logo' can be an answer for 'sign' (logo is a kind of sign). I am not certain of the 'the identifying' bit.
'a record circle' is the wordplay.
'a record' becomes 'log' (log is a kind of record).
'circle' becomes 'O' (O is a circle).
'log'+'o'='LOGO'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for logo that I've seen before include "Company emblem or device" , "Symbol or emblem used by organisation" , "Small design used as a company emblem" , "Vigour; relish" , "Brand's emblem" .)