The possessive form for the noun contractor is contractor's.

Examples:

The contractor's tools were at my house.

I am going to the contractor's building tomorrow to discuss the cost.

A contractor service agreement is an agreement between a contractor and a person or group that this contractor wishes to do work for. It states who the contractor and person or group is, the specifics of the job and timeline for the job, how much the contractor will be paid and what method of payment will be used to pay the contractor.

An insured contractor is a contractor who carries a Commercial General Liability Insurance Policy.

Traditionally the contractor provides the Insurance. The owner verifies that the contractor has insurance prior to hiring that contractor.

Anyone who does work for a general contractor and is not a direct employee of that contractor is a sub-contractor. Regardless of who sets the price. The subcontractors work within the contract set between the general contractor and homeowner. Hence sub-contractor.