Motivated by experimental results on transport properties of graphene covered by gallium atoms, the density functional theory study of clustering of gallium atoms on graphene (up to a size of 8 atoms) is presented. The paper explains a rapid initial increase of graphene electron doping by individual Ga atoms with Ga coverage, which is continually reduced to zero, when bigger multiple-atom clusters have been formed. According to density functional theory calculations with and without the van der Waals correction, gallium atoms start to form a three-dimensional cluster from five and three atoms, respectively. The results also explain an easy diffusion of Ga atoms while forming clusters caused by a small diffusion barrier of 0.11 eV. Moreover, the calculations show this barrier can be additionally reduced by the application of an external electric field, which was simulated by the ionization of graphene. This effect offers a unique possibility to control the cluster size in experiments only by applying a gate-voltage to the graphene in a field-effect transistor geometry and thereby without growth temperature assistance.