https://www.nolo.com/legal-encyclopedia/the-eviction-process-texas-rules-landlords-property-managers.htmlTerminating a Fixed-Term Tenancy Without Cause
A landlord cannot end a fixed-term tenancy early without cause. a lease guarantees tenants the right to stay at the property (so long as they don't violate its terms) for the duration of the time stated.
When landlords wish to have tenants with a lease move out without having cause (such as a failure to pay rent), they must wait until the term ends. However, the landlord is not required to give the tenant notice that the lease isn't being renewed, unless the lease specifically requires it. For example, if the tenant has a year-long lease that expires in December and the tenant has not requested a renewal, the landlord does not need to give the tenant notice to move out of the rental unit by the end of December (unless such notice is required in the lease). When December comes around, the landlord can expect the tenant to move out of the rental unit by the end of the month.
When tenants don't move out at the end of a lease, they become holdover tenantstenants who do not have the protection of a lease. To remove a holdover tenant in Texas, the landlord must give the tenant a three-day notice to vacate. If the tenant does not move out by the end of the three-day period, then the landlord can file an eviction lawsuit with the court. (Tex. Prop. Code Ann. 24.005 (2020).)
sounds like your renter is currently protected by their original lease. when it expires that is a different story but right now they have a lease and you must abide by the section above.