If you move after living in a leased home in Missouri for over 8 years, does the landlord have to replace the carpet.

Not unless it needs to be replaced, and in fact they don't have to replace it, if he needs it. Many of my rentals in MO
But if you damaged the carpet beyond normal wear and tear, they can charge you for damage to the carpet.

Why are you asking? Is the landlord charging you for replacing the carpet?