Utah law lets private employers adopt a veterans employment preference. If an employer has one, it has to be in writing, applied the same way to hiring, promotion and retention during a reduction in force, posted publicly at the workplace, and posted online if the employer has a website or advertises jobs on the internet.
There is nothing to apply for with the state. Check the employer’s workplace postings or website for a veterans preference policy, and ask about it when you apply.
Your discharge documents, which the employer may require as proof of eligibility for the preference.