In this paper the authors have proposed a new 3×3 reversible gate and also proposed the reversible combinational logic circuits with better optimized quantum cost, garbage outputs and delay. The proposed new reversible logic gate is used to design of reversible 1-bit comparator circuit and realization of different logic functions such as NOT, AND, NAND, OR, NOR, XOR, NXOR. The proposed new reversible logic gate is represented by quantum implementation. The quantum cost of proposed gate is 4. The quantum cost, garbage output and delay of proposed reversible 1-bit comparator circuit are 6 which is better w. r. t. previously reported results.