The tungsten carbide α-WC(0001) surface, an active system for the activation of H2 and important hydrogenation processes involving unsaturated hydrocarbons, can serve as a support of bimetallic clusters to produce materials with unique catalytic properties, opening routes for a wide range of technical applications. In particular, CuxPdy clusters are of particular interest because they combine metals with different properties. A stochastic method was applied to obtain the geometry of CuxPdy (x + y = 4) bare clusters, evaluating thousands of possibilities to obtain stable structures, yielding one isomer for Cu4, Cu2Pd2, Cu1Pd3, and Pd4 and two isomers for Cu3Pd1. These clusters were supported on C and W terminations of the tungsten carbide (0001) surface, exploring all of the binding possibilities. The adsorption energies on the C and W terminations are in the ranges from −2.51 to −3.02 eV and from −2.26 to −3.30 eV, respectively. The strongest and weakest binding was seen for monometallic Cu4 and Pd4 clusters on both C and W terminations, while the Cu-Pd bimetallics have intermediate adsorption energies but lack a clear trend in terms of composition. The location of CuxPdy clusters over the (0001) surface induces a decrease in the work function relative to the pristine surface, while the cluster-surface Bader charge transfer and variations in the partial density of states point to changes in the electronic structure of the carbide atoms upon binding of the metallic clusters. The d-band center of the CuxPdy deposited on WC(0001) indicates an intermediate reactivity among Cu(111) and Pd(111) surfaces, modulating the reactivity with small numbers of Cu and Pd atoms, i.e., atom economy in catalyst design. The likelihood of existence of the most stable CuxPdy (x + y = 4) clusters in the temperature range of 298-400 K is 100%. The composite CuxPdy/α-WC(0001) (x + y = 4), is a nontrivial system since 22 isomers are needed to completely describe its structural properties. Among the isomers, seven structures are necessary to represent Cu3Pd1/α-WC(0001), five for Pd4/α-WC(0001), two for Cu4/α-WC(0001), and four for Cu2Pd2/α-WC(0001) and Cu1Pd3/α-WC(0001). The large number of cluster isomers supported on the tungsten carbide surface opens the door for several applications in the heterogeneous catalysis of the CuxPdy/α-WC(0001) composite, with the possibility of modulating the geometric, electronic, and chemical properties according to a desired application. Test studies for the adsorption of CO2 indicate that the CuxPdy/α-WC(0001) composites are highly active for the adsorption and decomposition of the molecule, with bimetallic and admetal-carbide interactions playing a key role in the binding performance. This high activity indicates that these systems should be useful as catalysts for the conversion of CO2 to oxygenates or light alkanes. © 2025 American Chemical Society.