A week of gap in leases?

[Amanda G.]

If all goes well, I will close on a property on 2/23. The property already has tenants, who I am going to screen, and (hopefully) keep. I will get their rental applications later this week. Should I get leases in place with them before I close? That doesn't seem legal. How do I handle the gap between closing and 3/1, when I would collect a first month's rent from them?