A dispenser with a transfer assembly is arranged to efficiently transfer a stored liquid from a reservoir in a body of the dispenser to an applicator. The transfer assembly includes an adapter, applicator base, piston and a bias member. The adapter is in contact with the body and has a central member with orifices to fluidly couple the applicator base to the reservoir. The applicator base is supported by and extends beyond the adapter. The applicator base forms a cavity for housing the piston and the bias member. A tubular member of the applicator base supports an applicator. The piston includes a passage that conveys the stored liquid from the cavity to the applicator. The bias member keeps the head of the piston against a surface of the central member. When stored liquid is under a pressure that exceeds a bias force, displacement of the piston, opens a seal.