I purchased a duplex that came with one section 8 tenant that has been there for 1.5 yrs. Tenant is month to month and been wanting to move because old landlord didn't want to replace the carpet (worn out and super dirty). Tenant would stay and sign a new 1yr lease if I changed carpet and fixed some maintenance issues. Bottom line is either way I have to change carpet if tenant stays or if tenant goes but carpet is mostly dirty than worn out, so tenant is partially at fault. How should I proceed ? 

How is the tenant at fault? If you just bought it, you likely have no idea how old the carpet is.  Carpet has a lifespan. If its time to replace the carpet, thats your responsibility to do so, and fixing the maintenance issue is your responsibility as well.

@Russell Brazil , I do understand the lifespan of the carpet, and that's why I said tenant is partially at fault for not keeping it clean. 

Has the lease been transferred or are you going to have to put her in a new lease. (It depends on the paperwork you signed at closing.) If you have to put her in a new lease, you will be bound by a 12 month term by HUD. If not, you can set any lease term you and the tenant agree on. I have a property where grass won't grow well because of all the trees. I had a SEC 8 tenant with little boys, and it was inevitable the carpet was going to get cruddy. At renewal she said she wanted to leave because of the carpet. I offered to tear it out and put in luxury vinyl throughout if she signed a 5 years lease, and she agreed! That was 6 years ago, and she just moved out this year. The floors still look great! It was a win-win.

@Patti Robertson Great idea, and I had a similar idea. I told the tenant if they sign a new 2 yrs lease I will change the carpet at no cost but tenant said section 8 only allows 1yr agreement. I don't want the tenant to live in these conditions, either way I will change the carpet, I'm just asking  to see what options I have and what other landlords have done in these situations.

You can try having it cleaned to start with and if that doesn't work, have it replaced.  Is the carpet throughout the unit or only in a few rooms?  Replacing the carpet with a tenant in place is not simple as they have all their stuff in the home.  

Look at alternatives to carpet.  It might be a bit more at the beginning, but save you in the long run as there is less wear and tear.

I think it’s worth keeping the house looking nice. If it’s a good tenant, why not keep her? I mean, if you want to get rid of her, that’s another story.

I like @Patti Robertson suggestion about LVP. I’ve been putting it in my rentals. It’s a bit more expensive, but pretty much bombproof.

Good luck!

If you sign an Assignment of Lease Agreement at closing, I think SEC 8 should allow the current lease to remain in place with a new payee.  That would leave  you month to month though, so that's not a good scenario.  Maybe tell her you will pay for cleaning now but will replace them when she renews? Renew her early at the sixth month mark if all is going well.

I would recommend going with a vinyl plank. It's way more durable than carpet and depending on the style you purchase, it's not that much more expensive. Unfortunately, if you don't have a move-in inspection and pictures there isn't much much recourse for the dirty carpet. 

If the tenant is willing to sign a new lease (and she wants to move her around to accommodate new flooring installation) then I would install new flooring for her. I would first offer to have the carpets professionally cleaned and see if that will suffice.  

Are you attributing some of it to the tenant because the tenant keeps the place dirty?  I would be inclined to replace with LVT if the tenant is reasonably clean.