Organised push to get primate to improve (5,2)
I believe the answer is:
shape up
'improve' is the definition.
(thesaurus)
'organised push to get primate' is the wordplay.
'organised' is an anagram indicator.
'to get' is an insertion indicator.
'primate' becomes 'ape' (large primate).
'push' with letters rearranged gives 'shup'.
'shup' placed around 'ape' is 'SHAPE-UP'.
'to' is the link.
(Other definitions for shape up that I've seen before include "Develop in a particular way" , "Get fit" , "Come along" , "move forward" , "Advance!'" .)