We present a combined experimental and simulation study of the 4s -> 4p photoexcitation of the K atom trapped at the surface of ArN clusters made of a few hundred Ar atoms. Our experimental method based on photoelectron spectroscopy allows us to firmly establish that one single K atom is trapped at the surface of the cluster. The absorption spectrum is characterized by the splitting of the atomic absorption line into two broad bands, a Pi band associated with p orbitals parallel to the cluster surface and a Sigma band associated with the perpendicular orientation. The spectrum is consistent with observations reported for K atoms trapped on lighter inert gas clusters, but the splitting between the Pi and Sigma bands is significantly larger. We show that a large amount of K atoms are transiently stuck and eventually lost by the Ar cluster, in contrast with previous observations reported for alkaline earth metal systems. The excitation in the Sigma band leads systematically to the ejection of the K atom from the Ar cluster. On the contrary, excitation in the Pi band leads to the formation of a bound state. In this case, the analysis of the experimental photoelectron spectrum by means of nonadiabatic molecular dynamics simulation shows that the relaxation drives the system toward a basin where the coordination of the K atom is 2.2 Ar atoms on the average, in a poorly structured surface.