Yes, because a Will is an essential back-up device for property that you don’t transfer to your self as trustee. For example, if you acquire property shortly before you die, you may not remember to transfer ownership of it to your Trust, which means that it won’t pass under the terms of the Trust document. But, in your back-up Will, you can include a clause that names someone to get any property that you haven’t left to a particular person or entity. If you don’t have a Will, any property that isn’t transferred by your Living Trust or other probate-avoidance device (such as joint-tenancy) will go to your closest living relatives in an order determined by state law.
The person you appoint to handle the Trust after your death, the successor trustee, simply transfers ownership to the beneficiaries you named in the Trust. Much of the time, this can be accomplished in a few weeks, When all the property has been transferred to the beneficiaries, the Living Trust ceases to exist.