Question regarding leases

[Michael King]

BP friends, I have a question. I bought a 4 plex in January and took on the existing tenants and leases. My plan was to just let the leases expire naturally then replace them with mine. What could be a more brilliant plan?

Well I finished rehabbing one of the vacant units and let an existing tenant peek inside. She fell in love with it and wants to move in immediately (with a nominal rent increase). Her current lease expires in July, and the lease is an agreement with the prior owner. I'm thinking that I can't just terminate that lease, nor make an amendment to it since I'm not on it. So the dilemma is that she has an agreement for 1 apartment with someone else and now I want her in another apartment, and an agreement with me. How do I go about this?

I'm thinking I'll just start a fresh lease agreement between her and me in the new apartment, and let the old lease just run it course (obviously without enforcing any of it). Or should I provide a written notice terminating her current lease?

I guess in future with inherited tenants I should have the seller terminate all leases so I can go in and start my own leases. 

I feel like I'm running behind the short bus here.