In 1998, Kharlampovich and Myasnikov proved that if two subgroups of a hyperbolic group G satisfy certain conditions, then the associated HNN extension of G is hyperbolic. In this talk, I will first familiarize you with this result. Afterwards, I will present an alternative proof of the result under more restrictive assumptions, the basic approach of which is using the fact that a Cayley graph of the extension can be considered as a family of copies of a Cayley graph of G arranged in three shape.