If you are a Utah resident service member stationed outside Utah, your Utah driver licence stays valid until 90 days after you are discharged. The same extension covers your immediate family members and dependents.
There is nothing to apply for in advance. Carry your orders showing that you are stationed outside Utah, and renew your licence within 90 days of discharge.
Your orders stationing you outside Utah, and proof of your relationship to the service member if you are a family member.