Make progress in good school (3,2)
I believe the answer is:
get on
'make progress' is the definition.
(synonyms)
'good school' is the wordplay.
'good' becomes 'g' (abbreviation).
'school' becomes 'eton' (famous UK public school).
'g'+'eton'='GET ON'
'in' is the link.
(Other definitions for get on that I've seen before include "Board - prosper" , "Board; establish good relations" , "Make progress or advance in age" , "Age; prosper" , "Proceed; prosper" .)