Assistant's job to keep record (6)
I believe the answer is:
deputy
'assistant's' is the definition.
(both can mean a second-in-command)
'job to keep record' is the wordplay.
'job' becomes 'duty'.
'to keep' indicates putting letters inside.
'record' becomes 'EP' (abbreviation for extended play record).
'duty' enclosing 'ep' is 'DEPUTY'.
(Other definitions for deputy that I've seen before include "number two" , "Person appointed to act as substitute" , "US sheriff's assistant" , "Appointed representative for another" , "Assistant with power to act in the absence of superior" .)