Final answer:
The term for inserting a bud from one plant into another is called budding, which is a method of asexual reproduction used in horticulture to combine desirable traits.
Step-by-step explanation:
The term for inserting a bud from one plant into a cleft in the bark of another plant is called budding. This method of asexual reproduction is used in horticulture to combine the favorable traits of two plants to create a new individual with desired characteristics, such as a plant with both good root and shoot systems. For example, in viticulture, scions from European grape species that produce superior fruit are often grafted onto North American rootstocks that have greater disease resistance.