Different primates picked up speed (8)
I believe the answer is:
separate
'different' is the definition.
(thesaurus)
'primates picked up speed' is the wordplay.
'primates' becomes 'apes' (ape is a kind of primate).
'picked up' shows that the letters should be reversed in order.
'speed' becomes 'rate' (rate is a kind of speed**).
'apes' written backwards gives 'sepa'.
'sepa'+'rate'='SEPARATE'
(Other definitions for separate that I've seen before include "Divide, part" , "Split" , "Not joined or united with others" , "Standing apart" , "Pull apart" .)