The synthesis of a new microporous metal-organic framework (MOF) based on two secondary building units, with dinuclear cobalt centers, has been developed. The employment of a well-defined cobalt cluster results in an unusual topology of the Co2-MOF, where one of the cobalt centers has three open coordination positions, which has no precedent in MOF materials based on cobalt. Adsorption isotherms have revealed that Co2-MOF is in the range of best CO2 adsorbents among the carbon materials, with very high CO2/CH4 selectivity. On the other hand, dispersion of Co2-MOF in an alcoholic solution of Nafion gives rise to a composite (Co2-MOF@Nafion) with great resistance to hydrolysis in aqueous media and good adherence to graphite electrodes. In fact, it exhibits high electrocatalytic activity and robustness for the oxygen evolution reaction (OER), with a turnover frequency number value superior to those reported for similar electrocatalysts. Overall, this work has provided the basis for the rational design of new cobalt OER catalysts and related materials employing well-defined metal clusters as directing agents of the MOF structure.