Record time taken by primate (4)
I believe the answer is:
tape
'record' is the definition.
(I know that record can be written as tape)
'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 "broken by fastest runner" , "Race winning line; record" , "Bind" , "Fabric strip; record" , "Strip of material (that might be red!)" .)