Collective electronic excitations associated with a potassium monolayer (1 ML) on a Be(0001) substrate are studied using ab initio evaluations of the surface response function with the use of energies and wave functions obtained from the self-consistent pseudopotential calculations. The plasmon dispersion relations as well as real and imaginary parts of the dynamical induced charge density oscillations are presented. Comparison of the collective modes of the 1 ML K/Be(0001) system with that of a clean Be(0001) surface is given. It is shown that the K monolayer adsorption leads to appearance, additionally to the conventional surface plasmon of a clean Be surface, of a low-energy mode with characteristic acoustic-like dispersion in the 0-2 eV energy range. The existence of this mode owes to the presence of a K-induced quantum-well-state band whose wave function is strongly localized in the K adlayer. Also we observe a K-derived multipole plasmon with energy around 3 eV. Some other modifications in the Be surface plasmon properties upon K adsorption are discussed as well.