Anthropic's own frontend-design skill attempts to do that. You can install it in Claude Code, or you can tweak it to be closer to your own style:

https://github.com/anthropics/claude-code/blob/main/plugins/...

But what I find works best is to point Claude at a design system documentation website (your own company's or another public source) and tell it to use that design style. It usually does OK, and the results are usually much more in line with that style and not as Claude-y.