The archetypal minor prince
What could be better than literal royalty? And yet, for The Leopard, Prince Fabrizio di Salina, ultimate power is still not enough, because his supreme sovereignty is limited by the size of his territory. He is the archetypal big fish in a little pond, so his life leaves him with the desire to have more. His journey is not the empire building fate of the Italian kings. Rather, he endures the emotional journey of humiliation, removal from power, and ultimately he succumbs to true powerlessness when he dies.
Fabrizio's symbolic nephew
Whereas Fabrizio's life has become a narrative about power and authority, he has a happy, go-lucky nephew who gets to live a wonderful romance with a hot young princess. Their time is contrasted with the hopelessness and frustration of the prince's deposition, and thus it symbolizes the cruel hand of fate, because while he is old, powerless, and dying, his nephew is just hitting his stride, having the best days of his life. This is a symbol for the passage of time, because the nephew is replacing him.
The offer
There is a symbolic offer made when the prince yields his authority to the undeniable army of Italians. He knows to resist would mean to lose his life and the lives of all those in his kingdom. The symbolic offer comes as a consolation when he admits defeat. He denies it, which is a symbolic way of admitting true powerlessness. He doesn't even want to maintain the illusion of power. In a way, the denial of consolation represents a kind of honor. He has the humility to admit defeat.
The pregnancy out of marriage
When someone in his family becomes pregnant from a lover outside of marriage, that symbolizes the limits of social propriety. Although there are rules that humans obey for social reasons, there are rules of nature too, because humans are animals after all, and apparently the instinctual urge to make love was more pressing than the honor of the family. This symbolizes the limits of social propriety, which basically defines the royal life.
The symbolic ending
All the plots converge in Fabrizio's death. After a life of power, he endures a long life of powerlessness, going from royalty to normal life. But nothing matters in comparison to the symbolic ending of the story, which is his death. He realizes that the drama of his life and desire for political power was always a symbol for his fear of powerlessness in general. No man is powerful enough to stop their death, so he turns to God to ask for a peaceful afterlife, a symbol for the ubiquity of death and the futility of human endeavors.