Lease ends but tenant can’t move

[Marci Stein]

My tenant ( an excellent one ) of 2 years informed me she will not sign a new lease and wants to move , however , since no one is showing apartments now she would like to pay month by month until crisis ends. 
 I don’t want to be insensitive , but if she moves after the summer it is extremely hard to rent out the house and could have a 6 month vacancy . 
Not sure if I have a choice in this situation- any suggestions?

Thanks!