Metal-carbon nanoclusters (MCNs) are relatively new materials, interesting for both theoretical and experimental research. Design of experiments on the synthesis of nanomaterials with desirable functional characteristics requires the development of adequate microscopic models. Directed modification of the properties of these materials is based on the principle of structuring in a materials science: "from atom through a cluster to an amorphous or quasi-periodic structure". Such models are based on the information about the MCNs electronic structure, the nature of interatomic interactions of the nanomaterials, obtained both from the experiment data and by using the methods of quantum theory and modern computational methods [1-3]. MCNs have a shell structure, and the graphene layer is located on the periphery of such composite system, so that the metal cluster forms the MCNs core. In other words, graphene is coordinated with metallic clusters. So, as а result of a convergence of the transition metal atoms (such as Cu, Co, Ni, Pd, etc.) and the graphene to form a stable complex due to the overlap between the d-orbitals of transition metals and carbon  -orbitals. The condition for the stability of such systems is the existence of local minimum of the free energy. Stability, in a rather wide range of temperatures, manifest the clusters of transition metals in the graphene envelopes following types – the flat discs (quasi 2D), as well as the needle (quasi 1D) and globular (quasi 3D) complexes [1-4].    In this paper we propose the microscopic model describing the nonlinear dynamics of electron localized in 4-center (tetramer) metal core of MCN with a graphene shell, so that the MCN metal core Me4– contains the transition metal atoms (for example, Me = Cu, Co, Ni, Pd), which may have different oxidation degrees.    For two MCN metallic core configurations named further as linear and cyclic types the obtained system was solved numerically at the various sets of model parameters. For the MCN of linear type the external electric field has the direction along its longitudinal axis, and for the MCN of cyclic type – along the axis connecting the 1-st and 3-rd centers. Numerical calculations for the two configurations were obtained that the considered MCN, in which the centers is tunnel-connected and the electron-vibrational interaction with the ligand graphene environment at each of its centers is essential (case of a strong nonlinearity). Analysis of numerical calculation results showed that within the framework of the given model, changing the parameters of an external electric field, the variety of characteristic regimes in the electron localization dynamics can be implemented in the MCN: – The periodic regime of switching of the electron density between the 1-st and 3-rd centers of the cyclic tetramer and the 1-st and 4-th centers of the linear tetramer with a partial filling of the intermediate centers 2 and 4 in the cyclic case, and 2 and 3 in the linear case, correspondingly; – The regime with the effect of transparency of the intermediate centers;  – The locking regime of electron on the 1-st center. Management role of the electric field was revealed, allowing to realize how the regimes of electron localization and as well as the regimes of electron delocalization along the direction of the external electric field. It is shown as a variation of the frequency and amplitude of the field controls the duration of the full electron localization on the definite cluster centers and the cluster can be switched from a state with the localized electron to a state with the delocalized electron.