One of the most characteristic features of galaxy clusters is the so-called “red sequence” (RS) of early-type galaxies. Since these galaxies are, in general, devoid of gas and dust, their red colors are mainly a consequence of their passive nature. However, the physical mechanisms responsible for quenching their star formation, thus originating the RS, are poorly understood. Environmental effects should play a significant role in the formation of the RS by transforming the observed galaxy properties from late to early-type ones. In this respect, we have initiated a KMOS program aimed at studying the kinematical structure of cluster galaxies at 0.8 < z < 1.7 in an effort to disentangle the physical mechanisms responsible for cluster galaxy evolution and the formation of the RS.