Which Dornish princess was omitted from the TV series?

The Dornish princess omitted from the Game of Thrones television series was Arianne Martell.

Arianne is the eldest child of Prince Doran Martell and the heir to Dorne in the novels. She first appears in A Feast for Crows, where she fears that Doran intends to replace her with her younger brother Quentyn. Her concerns lead her to plot the crowning of Myrcella Baratheon as queen, taking advantage of Dorne’s inheritance customs, which favor the eldest child regardless of gender.

Doran stops the plan before it succeeds and explains that he has been pursuing a secret strategy against the Lannisters. Later, he sends Arianne to investigate Aegon Targaryen and the Golden Company. That entire political storyline was absent from the show.

Some of Arianne’s narrative functions were loosely transferred to Ellaria Sand, but Ellaria is a different character with a very different personality and fate. Myrcella and Ellaria both appear on television, making them tempting but incorrect choices.