Due to the unique properties of rare-earth (RE) metals, RE catalysts demonstrate distinctive catalytic performance in hydrogenation and related transformations. In typical RE catalytic systems, the roles and function modes have been studied and are relevant to ligands. In recent years, heterobimetallic catalytic systems have emerged for efficient hydrogenation and related transformations. Among these systems, heterobimetallic catalysts with transition metal (TM)-RE combinations integrate the characteristics of TM catalysis and RE catalysis, exhibiting a TM-RE bifunctional effect with remarkable activity and selectivity. However, the roles of RE metals in TM-RE bifunctional catalysis remain ambiguous. This theoretical study takes the Ni–Y system as a study case, aiming to elucidate the significant roles of the RE center in the TM-RE bifunctional effect on catalytic alkyne semihydrogenation. The results suggest that dynamic coordination can occur at the Y center due to its large size and coordination ability, which accepts the binding of phosphine groups of the ligand. The dynamic coordination of phosphine groups to the large-size RE center assists the Ni center in releasing vacant sites for substrate in-cage binding and reduces the steric effect on the Ni center. Meanwhile, the Lewis acidic RE center can stabilize the bridging hydride, which is crucial for H2 activation and hydrogenation. The TM-RE bifunctional effect promotes the reaction. During the H2 activation stage, due to the stabilization of nickel hydrides by yttrium, the fac-pathway is more favored. The Ni–H–Y bridging structure is maintained during the initial hydride insertion in the semihydrogenation stage, which is crucial for the reaction. Additionally, the use of the more active terminal hydride makes the terminal hydride pathway a more plausible mechanism. Benefiting from the capability of yttrium to accept the dynamic coordination of phosphine groups, thereby releasing steric hindrance and stabilizing the bridging hydride concurrently, (Z)/(E)-isomerization can proceed to achieve (E)-selectivity through the H2-assisted Ni–Y bifunctional pathway with a relatively low energy barrier. Owing to the RE-bridging hydride stabilization effect, the thermodynamic properties of intermediates are closely related to the size of the RE metal center, thereby influencing the activity and the (Z)/(E)-selectivity. These results underscore the important roles of the RE center in TM-RE bifunctional catalysis, offering valuable insights into the future design of effective bifunctional TM-RE catalysts.