Esmeralda is the name of Lavender’s older half-sister. She is the daughter of the king and his first wife, another queen who died before Lavender was born. She had two children, both girls. As the king said earlier, both are presumably dead. Amaranth here is his second wife, and she has three children. You’ve met only two so far: Lavender and Prince Argotta.
So for those of you keeping track, here’s a list of the royal children from oldest to youngest:
Princess Crimson (1st Queen) (dead)
Princess Esmeralda (1st Queen) (supposedly dead)
Princess Saffron (Amaranth) (secluded in a manor)
Princess Lavender (Amaranth) (secluded in a manor until her escape)
Prince Argotta (Amaranth) (confined to royal operations)
Who Esmeralda is and why she is important will be explored in the next chapter of the story.