Little time to copy record (4)
I believe the answer is:
tape
'record' is the definition.
('tape' can be a synonym of 'record')
'little time to copy' is the wordplay.
'little time' becomes 't' (abbreviation for time).
'to copy' becomes 'ape' ('ape' can be a synonym of 'copy').
't'+'ape'='TAPE'
(Other definitions for tape that I've seen before include "Measure" , "Common medium for recording" , "Video recording" , "Record; material strip" , "that race winner may break" .)