What we learn by accepting established award (7)
I believe the answer is:
rosette
'award' is the definition.
(I've seen this before)
'what we learn by accepting established' is the wordplay.
'what we learn by' becomes 'rote' (as in 'learning by rote').
'accepting' means one lot of letters goes inside another.
'established' becomes 'set' (I've seen this in another clue).
'rote' enclosing 'set' is 'ROSETTE'.
(Other definitions for rosette that I've seen before include "Prizewinner's decoration" , "Cockade" , "Decoration made of ribbons" , "Ribbon in a cluster as an award" , "collection of ribbons" .)