Certified GKH Gardening Expert
Generally, they should be transplanted during late winter or early spring when they are not actively growing for more successful results. If it is a relatively small one with trunk diameter of 4" or less, moving the plant shouldn't be a big problem.
First, remove all but the uppermost ring of leaves - this will help reduce transplant shock to the roots. Then dig about 6" away from the trunk and at least 12" deep, getting as much of the root system as possible. Gently pop it out of the ground. Move the plant to a pre-dug hole slightly larger than the root-ball of the plant. After transplanting, water it thoroughly and then only water when the soil becomes nearly dry.
If it is a large palm, with a trunk diameter of 6" or more and trunk height of over 12", use the same procedure above, but dig a larger, deeper root-ball and hole or call in a professional.
This article will help in reducing transplant shock: https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm