According to KUTV, someone has introduced bills to require a home inspector license in Utah in 2003 and 2006. But neither bill became law. So as of the time of this 2017 article, there was still no requirement for home inspectors to get a license at the state level. You should still check for any local requirements.
It is important to distinguish between a licensed building inspector and a home inspector. A building inspector is licensed to do code enforcement. When it comes to residences, that usually means a newly constructed home. But a home inspector is usually called in to inspect for defects in a house that is being sold to a new owner. So these unlicensed home inspectors examine “used” homes instead of new ones. If you want to inspect older homes before they are sold, then you don’t need a license to do this in Utah. But if you are considering getting qualified as a building inspector, you can use the following resource page to find laws, rules, application forms, and the like.
Since there are no requirements to operate, there are also no qualifications to become a home inspector in Utah. However, it would not be wise to just suddenly open shop and offer home inspection services. You might be able to competently do that if you are experienced in the construction industry or are already a licensed building inspector. Otherwise, though, it would behoove you to get some training and perhaps get certified before you start a home inspection business. This will give you added credibility that may be helpful in getting more clients.
A lot of inspectors network with real estate agents or attorneys since home buyers are typically already in contact with these other professionals before they even think of ordering a home inspection. To network with real estate brokers and perhaps attorneys, you really want to be certified to give those other professionals confidence that you will do a professional job if they refer you.
While I cannot recommend any specific associations that train and certify home inspectors at the national level, I can give you a list of some for your convenience.
Utah Building Inspectors Training Program (not for home inspectors, but included here if you are interested in a building inspector license)