Does a landlord have to replace carpet in ohio after 7 years living here and it wasn't new when moved in

There is no law that requires landlord to replace carpet. But if landlord wants to do it, and you don't cooperate, then landlord might choose not to renew your lease when it expires, forcing you to move out, so the carpet can be replaced then. You could hire somebody to move furniture around if necessary.

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I am no OH attorney, but suspect that if LL wants to replace carpet (which LL is free to do) that the LL can also pay to have someone move the furniture if you cannot for valid health reasons. If you don't want new carpet you might be able to tell the LL to skip your unit for now. You can also get an OH attorney to help you negotiate with the LL.