An Arkansas contractor taking work in Alaska 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 Alaska's answer to each, with the agency's own link.
Licensing
DCCED Division of Corporations, Business and Professional Licensing, Construction Contractor Section
Contractors must register with DCCED: surety bond ($25,000 general; $20,000 general with residential endorsement; $10,000 specialty and mechanical; $5,000 handyman for projects $10,000 or less), liability insurance, and workers' comp. Residential contractor endorsement requires a 16-hour cold-climate course plus exam.
https://www.commerce.alaska.gov/web/cbpl/ProfessionalLicensing/ConstructionContractors.aspx
Workers compensation
Alaska Dept. of Labor and Workforce Development, Division of Workers' Compensation
Every employer with one or more employees in Alaska must carry workers' comp; sole proprietors, partners, and 10-percent-plus owner-officers and LLC members are excluded from mandatory self-coverage.
Business registration
Dept. of Commerce, Community, and Economic Development, Division of Corporations, Business and Professional Licensing
Tax registration
Alaska Department of Revenue, Tax Division
No state sales tax or individual income tax; local municipal sales taxes may apply.
New hire reporting
Most states require newly hired employees to be reported within a short window of their start date.
https://childsupport.alaska.gov/child-support-services/employers/employer-information
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Starting or running the business itself is covered in the contractor business guide. Arkansas licence records for Benton and Washington counties are in the contractor directory.