Collocations for greatness - noun

true
This book tells you nothing about the true greatness of his paintings.

future, potential
The Puerto Rican was tipped for future greatness.

former
artistic, literary
national
He was made into a symbol of national greatness.

presidential (esp. AmE)

achieve
those people who have achieved greatness

be destined for
a woman who was destined for greatness

lie
Her greatness lies in her deep understanding of human nature.