Wise words show real brains, primarily (7)
I believe the answer is:
proverb
'wise words' is the definition.
(a wise saying)
'show real brains primarily' is the wordplay.
'show' becomes 'prove' (proving is a kind of showing).
'primarily' indicates taking the first letters.
The first letters of 'real brains' is 'rb'.
'prove'+'rb'='PROVERB'
(Other definitions for proverb that I've seen before include "Maxim" , "Pithy saying expressing a general truth" , "Familiar saying" , "Old saw" , "'Adage, saw (7)'" .)