Berserk (1997) features a subplot regarding the politics of the Midland monarchy.

Code Geass: Lelouch of the Rebellion

Cross Ange: Rondo of Angel and Dragon

Gankutsuou has no actual royals, but is filled to the brim with drama surrounding nobility.

Le Chevalier d’Eon

The Rose of Versailles

Sailor Moon features royal drama as a subplot.