Claire had never been jealous before meeting Saria. She didn't see anything as special enough to that, and even her relationship with her siblings, including Naomi, never made her feel that way.
And then she met the Mermaid Princess just as she finally accepted the greedy feelings in her heart. She finally understood that she wants a lot of things not just because of Greed but for herself too.
But what kind of things does she want? Everything is the answer. Starting with the attention of the most special girl she's ever met, Saria, obviously.
The Mermaids Princess is as beautiful and charming as she is kind and friendly. She awakened in Claire desires she was unaware of. That is a different friendship from the one she had with Naomi.
Everything seemed to be going perfectly well; Greed was pleased with how her plans were going, and Claire was becoming more and more intimate with Saria.