The Palace Museum recently exhibited cultural relics newly unearthed more than 2,000 years ago.

You don't have to worry about other problems here, you just need to see:

The Palace Museum recently exhibited cultural relics newly unearthed more than 2,000 years ago.

Cultural relics unearthed more than two thousand years ago are on display today.

So it should be changed to:

The Palace Museum recently exhibited cultural relics newly unearthed more than 2,000 years ago.

Cultural relics were unearthed more than 2000 years ago and are on display today.

I hope my answer is helpful to you. Good luck!

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Timely adoption, thank you.