A novel CCA was designed by substituting Nb in (FCC + C14 Laves) CoCrFeNi2.1(Nb)0.2 CCA by (Hf + Nb + Ta). The (HfNbTa)0.2 CCA was homogenized, heavily cold-rolled, and isothermally annealed at 800 °C and 1000 °C for different time intervals. The (HfNbTa)0.2 alloy revealed the presence of a Hf and Ni enriched cubic C15 Laves phase. The considerations of site occupancy behavior, formation energy, and highly off-stoichiometric composition stabilized the (Hf, Ni) rich cubic C15 Laves phase. In contrast to the brittle hexagonal C14 Laves phase in (Nb)0.2 CCA, the C15 Laves phase in (HfNbTa)0.2 CCA showed exceptional deformability owing to the high propensity for nano-twin formation. Meanwhile, the FCC matrix developed a deformation-induced nano-lamellar structure with a spacing of ∼45 nm. Annealing resulted in ultrafine recrystallized FCC matrix and precipitation of DO19 structured ε nano-precipitates. The isothermal grain growth kinetics revealed a high grain growth exponent (n) ∼7, which confirmed a Zener-drag mediated process due to the ε nano-precipitates. The Hall-Petch analysis of the hardness data showed relatively high friction stress originating from the dissolution of Hf, Nb, and Ta in the FCC matrix. A high Hall-Petch coefficient indicated increased shear stress for plastic flow across the boundaries, resulting from the elongated Laves phase at the boundaries. The highly deformable Laves phase, ultrafine grain size, and ε nano-precipitates resulted in high yield strength (∼975 MPa) and superior ductility (∼16 %) in the (HfNbTa)0.2 CCA, even surpassing the (Nb)0.2 CCA. It was envisaged that strong yet deformable Laves phases could pave the pathway for developing Laves phase-based CCAs for advanced structural applications.