Find 1314 flexible and convenient short-term apartments for rent in Salt Lake City. This Salt Lake City Housing group frequently has people looking to fill shorter leases.We offer lease terms from 2-15 months. When your initial lease term expires, you may choose to renew your lease or continue on month-to-month. You and your roommate(s) can fill out and sign the form before you move in together. This state-specific Lease is customizable and includes UT laws. Room is available Now. Utah state law requires a written agreement for terms that are longer than twelve months. If you're on a month-to-month lease, you usually must give one month's notice before you can stop paying rent. A shortterm lease agreement refers to a contract that goes monthtomonth, a period of three months, or any term of up to six months.