Relaxation dynamics following photoexcitation of a calcium atom deposited on an icosahedral-like argon cluster Ar-n (n approximate to 55) is investigated through theoretical simulations. Based on ab initio calculations of the CaAr molecule, a diatomics-in-molecules model is set up to efficiently describe the electronic excited states of the system. The excited state dynamics is studied using molecular dynamics with electronic transitions (Tully, J.C. J. Chem. Phys. 1990, 93, 1061). The signature of this dynamics in the time-resolved photoelectron spectra is investigated, to assess the possibility of detecting competing vibrational and electronic relaxations through pump-probe experiments. The vibrational relaxation, influenced by nonadiabatic transitions, can clearly be seen in the time-resolved photoelectron spectra. The details of the electronic relaxation, as well as the possible ejection of the chromophore, are found to be sensitive to the local environment of the calcium atom deposited on the argon cluster.