Termites are known to eat dead wood. If termites are infesting a live tree, then something is causing the tree's cambium layer or the pith of the tree to die. For long-term termite repellent, you should have an arborist look at your tree. In the meantime, there are a few things you can do to kill termites without harming the tree itself.
Examine the tree for any exposed termite galleries. These are spaces in the wood that termites have hollowed out.
Dig a trench that is 4 to 6 inches deep around the tree with a trenching tool.
Measure the length of the trench.
Purchase a broad-spectrum insecticide that is formulated to kill termites without damaging live wood.
Put on protective gloves, clothing and breathing protection before handling poisons such as the kind found in insecticides.
Following the instructions on the package of your insecticide, use the measurement of the length of your trench to calculate how much insecticide to apply to the trench. The amount of insecticide will vary depending on the brand that you use. Apply insecticide in the trench and allow it to soak into the soil.
Spray insecticide on the trunk of your tree, into termite galleries and on any mud tubes that you encounter. Termites build mud tubes so that they do not have to travel in the open air.