This work outlines a straightforward mechanism for endorsing primary hair into Schwarzschild black holes, resulting in a unique modification within the framework of a special scalar -tensor theory, the socalled beyond-Horndeski gravity. The derived solutions are exact, showcase primary hair with a regular scalar field profile everywhere, and continuously connect with the vacuum geometry. Initially devised to introduce primary hair in spherically symmetric solutions within general relativity in any dimension, our investigation explores the conditions under which spherically symmetric black holes in alternative gravitational theories become amenable to the endowment of primary hair through a similar pattern. As a preliminary exploration, we embark on the process of endowing primary hair to the Reissner-Nordstrom black hole. Subsequently, we extend our analysis to encompass spherically symmetric solutions within Lovelock and cubic quasitopological gravity theories.