Buying duplex with tenants whose lease expires soon

[Joe T.]

I'm currently in the process of buying a duplex that is currently occupied on both sides. One of the leases ends shortly after my closing date. I'm pretty sure that the existing tenant wants to stay, but I need to increase the rent on that side to meet market value (it's about $80 below). My question is, how do I make sure that I'm able to increase the rent if the tenants decide to stay, because the current owner will probably go ahead and extend their lease but I will not be the owner at the time.