Tenant added to lease/renewal

[Rebekah Nation]

Hi! I was hoping you all could provide some input. I’m a nurse and bought my first residential rental a little over a year ago so this is all very new to me.

I have a decent tenant in place (was in place when I bought the home). He has some quirks, but he fixes small things, calls about big things, pays on time so he is really a good tenant that I want to keep. His lease is up so we are discussing lease renewal and he wants to add his niece to the lease because she is currently living in a hotel. I told him that she has to fill out a rental application so I can run my background checks on her before adding her to the lease. He isn’t happy about that, but from everything I have read, anyone living in the house (over 18) should be on the lease and I would like to know basic information about her. Is this the correct thing to do in this situation? From the things I do know about her, I can’t imagine she would be a model tenant, but if she passes the background checks, I would add her to keep my current tenant. HOWEVER, I want to add something in the lease to the effect of, “if either tenant vacates property for any reason (to include death), other tenant must meet income qualifications to keep lease valid” so that if my tenant dies (my biggest fear- he’s in his 60s), I can boot her out if she is a trouble tenant because she wouldn’t meet income requirements on her own. Is this legal and does anyone have an appropriately worded lease clause for that? Thank you for all of your time and input.