She is just afraid she will lose her time with her as she gets invested in the club. Jealous that something else is taking time away from them being together. Kind of obvious. I expected her to to say she was doing a good job at being a prince.
In addition to that, she also seems to be spiraling a bit by comparing herself unfavorably to Takamine's involvement in the drama club. From her perspective, Takamine is this amazing person who's putting herself out there and doing all these cool things, and she let her own club wither away and isn't doing anything really interesting at all.
Now, that's not fair to herself, of course, and I'm sure she'll be informed of that sooner rather than later by Takamine in a suitably cute fashion, but you can get where she's coming from.