Well, can I?
Sure, put it in your lease that the renter is leasing only the living area and not the attic or crawlspace.
Any ideas on this with a currently leased home?
Create a lease addendum and have your tenant sign it. However, you can’t force them to sign so you may need to offer some incentive.
just talk to them and let them know. it is your house.
You can’t make a material change to the lease during the lease term unless the tenant agrees. I don’t know if this would constitute a material change or not. If it’s a tenancy at will, terminate the existing agreement per your state’s laws and offer a new tenancy with the new terms.
Why don’t you want them in the attic? One way to get them to go into the attic is to tell them that you don’t want them in the attic. If you hid the treasure chest filled with gold there I can guarantee that they will find it.