Tennessee Newbie

Florida resident, but planning to move eventually to middle Tn. About to close on 1st investment property- a triplex. How do I get the last remaining tenant, a complete slob, out of there? One unit is vacant and clean, the other folks are moving to a larger apr andkeep it real clean, too. It’s a disaster area in the last unit?
No existing lease, according to listing agent. HELP??
We want the place to be looking good when we show prospective tenants…
THANKS!

Not sure on Tenn law, but from our local attorney:

If there is no lease they are basically on a month to month lease. Give them the required notice for your area - here in Kansas City it is 30 days. If they do not comply evict them.

As you are new at this, hiring an attorney would be money well spent to walk you through this.