Recording time taken by primate (4)
I believe the answer is:
tape
'recording' is the definition.
(I know that tape is a type of recording)
'time taken by primate' is the wordplay.
'time' becomes 't' (abbreviation).
'taken by' is a charade indicator (letters next to each other).
'primate' becomes 'ape' (large primate).
't'+'ape'='TAPE'
(Other definitions for tape that I've seen before include "Common medium for recording" , "This is often stretched across the finishing line of race" , "Video recording" , "Sticky strip" , "that race winner may break" .)