Two questions often get mixed together when a home repair is being planned. The first is whether the service contract allows a particular person to do the work. The second is whether the law allows that person to do it. A contract's approval does not answer the second question, and the law's permission does not answer the first. Keep the two apart when you plan a repair.
Which kinds of work often need a license
In many places, work on gas lines, electrical circuits, and some plumbing and heating or cooling systems is reserved for licensed trades. The rules differ by state and often by locality. Many states also have an exemption for owners doing certain work on the home they live in, and that exemption frequently has limits, such as rental property or work done before a sale. Check the licensing board for your state and the permit office for your locality. The state pages on this site name the regulator for service contracts, which is often a different body from a trade licensing board, so check both.
Ask the contract administrator in writing
Ask whether a person who is not on the administrator's list will be accepted for the work, and whether the administrator needs a license number or proof of license before the work starts. Keep the answer with your contract. A verbal yes at the phone is not a record you can rely on later.
Ask the tradesperson directly
Ask for the license number and check it with the issuing board. Ask whether a permit is needed for the work and who pulls it. Some work needs a permit and an inspection no matter who performs it, and the permit record can matter when you sell the home or make a later claim.
A plain caution
This is a general explainer, not legal advice. For a specific job, ask the licensing board, the permit office, or a licensed professional who knows the local rules. The state pages on this site say which statute or program each state's rules come from and mark the states this edition has not read.