"great destiny" is a correct and usable phrase in written English.
You can use it to emphasize the future that someone or something has. For example, "She has a great destiny ahead of her."
He was sure that a great destiny awaited him.
Gaullism and Communism kept up the illusion that a great history, a great destiny were still France's to be had.
She radiates Hilde's feverish desire to fulfill a great destiny, although Ms. Parry could profitably tone down the scornful impetuousness.
Non, non, France must understand she has a great destiny if she is prepared for it," he said.
Lady Jessica, a witch (the good kind) steeped in the ancient ways, knows that her son has some great destiny to fulfill.
What she left, besides a staggering inventory of choice possessions that took a team of notaries a year to appraise, is a mystery still worthy of contemplation: did Pompadour fulfill a great destiny or betray one?
But as with all great destinies, there's always a choice.
The story begins in Manoka, Cameroon, where, on the morning of August 20, 1940, an artillery captain in the French colonial army, gripped by one of those spur-of-the-moment decisions on which great destinies are sometimes built, decides to follow an unknown general, Philippe Leclerc de Hauteclocque.
Few of us, though, have the sense of greater destiny to embark on such a quest.
Over and over women heard in voices of tradition and of Freudian sophistication that they could desire no greater destiny than to glory in their own femininity.
It is a larger one than it looks, since it is scarcely conceivable that batka (father) does not imagine for himself some greater destiny than running pocket-sized Belarus.
