Can they fill an application on line and is there a fee?

Yes, owners of construction businesses are required to carry workers’ compensation coverage on themselves or be listed on the Secretary of State’s Exemption Registry.  There are a few exceptions, for example, Construction Services Providers who work directly for a property owner with no subcontractors; or Construction Services Providers who work on their own property; or where the employment of the Construction Services Provider is casual labor.

See Tennessee Code §50-6-902.  See the Secretary of State’s Exemption Registry web link: 
https://tnbear.tn.gov/wc/ExemptionRegInstr.aspx

See also: https://sos.tn.gov/products/business-services/workers-compensation-exemption-registry-faqs

Tennessee Department of Labor/Bureau of Workers' Compensation