You can agree to rent your new home back to them, as a part of the Purchase and Sales agreement, by way of addendum. Ask your agent to draft this up for you, and it will require a lease agreement to protect your interests. They would have to abide by certain conditions set by you, the new owner--in order to stay.
OR, you can choose not to let them stay, if you wish to get into your new home upon closing, which you have every right to-
OR, you can extend the closing date to accommodate their need to stay. This would put the cost of mortgage, taxes, insurance, etc., back to them until they are out of the home at closing.
Of course, I am answering this from Idaho, and I see you are in Virginia, so please check with your local real estate professional, and/or attorney, for allowances within the existing contract, which may be different for you, relative to your real estate laws in Virginia.