No, renters insurance doesn’t cover early lease termination. Renters insurance provides several types of coverage, including personal property and personal liability coverage, but no type of renters insurance coverage will reimburse you for fines or penalties (such as the loss of your security deposit) imposed by your landlord if you break your lease early.
However, although renters insurance doesn’t protect you from the direct consequences of terminating your lease, renters insurance covers moving. If you move out of your current residence earlier than planned, your policy will follow you to your new home — just make sure to contact your insurer and let them know that you’re moving. There’s no need to buy a new renters insurance police unless your insurer tells you that they don’t offer coverage in your new location.