Enhancing redox activity at electrode–electrolyte interfaces by dispersing redox additive(s) in electrolytes is a recent approach to increase the specific energy of carbon supercapacitors. Here, we prepared a non-aqueous gel polymer electrolyte (GPE) incorporated with an ionic liquid (IL) 1-butyl-3-methylimidazolium bis(trifluoromethane sulfonyl)imide and dual redox additives (KI and diphenylamine, DPA) entrapped in a host polymer poly(vinylidenefluoride-co-hexafluoropropylene) for use in the fabrication of carbon supercapacitors. A free-standing film of the GPE with dual redox additives shows excellent flexibility, thermal stability (up to ∼320 °C), high ionic conductivity (σ_RT ∼ 4.52 mS cm⁻¹) and a wide electrochemical stability window (∼6.2 V versus Ag), indicating its suitability as an electrolyte in quasi-solid-state supercapacitors. The supercapacitor fabricated using the redox-active GPE (containing KI and DPA) and biomass-derived activated carbon electrodes exhibits superior performance over the devices with GPEs containing a pure IL or its mixture with a single additive (DPA or KI). The synergistic effect of dual redox activity at the interfaces leads to optimum specific energy (∼73.2 W h kg⁻¹) and maximum power (∼34.8 kW kg⁻¹), attributable to enhanced specific capacitance (∼337 F g⁻¹) and reasonably high operating voltage (2.5 V). The optimized capacitor shows good performance for ∼6000 charge–discharge cycles after a 20% fade in capacitance and maintains a coulombic efficiency as high as 98–100%.