An Arkansas contractor taking work in Tennessee deals with the same four questions everywhere: who licenses the trade, when a licence is actually required, when workers compensation kicks in, and where the business registers. Below is Tennessee's answer to each, with the agency's own link.
Licensing
Tennessee Board for Licensing Contractors (Dept. of Commerce & Insurance)
License required when total project cost is $25,000 or more, including electrical, plumbing, HVAC and roofing subcontracts over $25,000 (masonry $100,000 and up). Home improvement license covers $3,000 to $24,999 residential remodels in nine adopting counties.
Workers compensation
Tennessee Bureau of Workers' Compensation (Dept. of Labor & Workforce Development)
Construction businesses must carry coverage for everyone, including business owners; other employers need insurance at five or more employees.
https://www.tn.gov/workforce/injuries-at-work/employers/employers/who-must-carry-insurance.html
Business registration
Tennessee Secretary of State, Division of Business Services
Tax registration
Tennessee Department of Revenue
https://revenue.support.tn.gov/hc/en-us/articles/360057120152-GEN-1-Registering-A-New-Business
New hire reporting
We could not confirm a new hire reporting site.
Most states require newly hired employees to be reported within a short window of their start date.