Contemporary system-on-chip-based applications are battery-powered. To increase the operation time, they need various low-power/energy circuits. Carbon nanotube field-effect transistor (CNTFET) is a potential alternative to complementary metal-oxide-semiconductor for power/energy-efficient circuits implementation due to its high performance. Another way to reduce power/energy consumption in a circuit is to use multiple-valued logic, especially ternary logic, which has three logical states. This paper presents a novel 1-trit ternary multiplier circuit with 23 transistors based on only unary operators of the ternary logic system and the dual-supply voltages technique. The proposed design does not use the ternary decoder/encoder, logic gates, cascading transmission gates, and ternary multiplexer to reduce the transistors count, delay, power, and energy. The Stanford CNTFET model in the 32-nm technology node is used to simulate the proposed design. The delay, power, and delay-power-product (PDP) of the proposed design at 0.9V are 0.026ns, 0.139μW, and 3.614aJ, respectively. It offers improvements between 50% and 61.19% in delay and between 52.72% and 59.75% in PDP compared to previously published multiplier circuits, which are based on the dual-supply voltages and use 23 transistors. These improvements make the proposed design a good candidate for the design of the next generation of multiplier circuits in arithmetic blocks.