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 Π band associated with p orbitals parallel to the cluster surface and a Σ 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 Π and Σ 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 Σ band leads systematically to the ejection of the K atom from the Ar cluster. On the contrary, excitation in the Π 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.