I had to cancel my rental insurance in 2023 to move and repay for the new one for NM? Does this count as a less common expense? I had to move for work?

Moving expenses are not deductible on a federal tax return except for certain active duty members of the military.    Changing your renters insurance was a personal expense that is not deductible.

Per the tax laws that changed for 2018 and beyond, moving expenses are not deductible on a federal return except for certain active duty members of the military.

There are several states that allow a deduction for moving expenses on the state return:  AZ, AR, CA, HI, IA, MA, MN, NJ, NY, PA and VA  You can enter your moving expenses in the federal software and the information will flow to your state return.