Two-dimensional (2D) carbides, nitrides, and carbonitrides known as MXenes are emerging materials with a wealth of useful applications. However, the range of metals capable of forming stable MXenes is limited mostly to early transition metals of groups 3-6, making the exploration of properties inherent to mid or late transition metal MXenes very challenging. To circumvent the inaccessibility of MXene phases derived from mid-to-late transition metals, we have developed a synthetic strategy that allows the incorporation of such transition metal sites into a host MXene matrix. Here, we report the structural characterization of a Mo2CTx:Co phase (where T-x are O, OH, and F surface terminations) that is obtained from a cobalt-substituted bulk molybdenum carbide (beta-Mo2C:Co) through a two-step synthesis: first an intercalation of gallium yielding Mo2Ga2C:Co followed by removal of Ga via HF treatment. Extended X-ray absorption fine structure (EXAFS) analysis confirms that Co atoms occupy Mo positions in the Mo2CTx lattice, providing isolated Co centers without any detectable formation of other cobalt-containing phases. The beneficial effect of cobalt substitution on the redox properties of Mo2CTx:Co is manifested in a substantially improved hydrogen evolution reaction (HER) activity, as compared to the unsubstituted Mo2CTx catalyst. Density functional theory (DFT) calculations attribute the enhanced HER kinetics of Mo2CTx:Co to the favorable binding of hydrogen on the oxygen terminated MXene surface that is strongly influenced by the substitution of Mo by Co in the Mo2CTx lattice. In addition to the remarkable HER activity, Mo2CTx:Co features excellent operational and structural stability, on par with the best performing non-noble metal-based HER catalysts. Overall, our work expands the compositional space of the MXene family by introducing a material with site-isolated cobalt centers embedded in the stable matrix of Mo2CTx. The synthetic approach presented here illustrates that tailoring the properties of MXenes for a specific application can be achieved via substitution of the host metal sites by mid or late transition metals.