First Rental Property Closing In Days

[Troy B.]

I'm about to close on my very first investment rental property in about five days. It is a two unit duplex and one is currently rented, the other needs a few repairs and should be ready to rent in a month. The current renter wants to stay, but is under paying for rent in this area. I assume getting him to sign a new lease would be my first priority. My question is what else should be done in the first few days after closing?