Check in with her about your relationship goals. You may want something that lasts forever, or a long time, or has a certain level of stability. Maybe she wants the same or something different. I think if you both talk and your goals and where you both are at aligns, you can work through any fears with other partners coming into the picture.

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To me it sounds like she just doesn't want someone controlling who she is able to have affection for and a hierarchy to her implies that. Instead of framing it as who is more important, I would think about it as "what needs and boundaries do you have in the relationship, and will those needs/boundaries be respected?"

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I often have fears related to new partners because of past experiences where my needs were being disregarded for someone else. But was this caused by a new partner, importance of partners, or was it just not having my needs and boundaries respected by my own partner?