I’m not sure about extension. But we’ve a discussion about this here https://community.brave.com/t/please-keep-the-tabs-where-they-are-under-the-address-bar/32353/9?u=eljuno
And we also have an open issue about this.
Currently there’s no option available for that – to customize Nee Tab Page. The team is working on it.
If you want, for now, you can install extension to override Brave’s NTP.