Remove your agapanthus from its current container. If it will not come out easily, run a flat-bladed knife around the edge of the root ball to loosen it. If you are repotting it into a same-sized pot, remove 2 inches of bulbs from the diameter of the clump to give it a 1-inch space all around to spread. Choose a container 2 inches larger in diameter if you are keeping the clump intact. Fill the new container half full with a well-draining potting mix that is rich in organic matter, such as an African violet mix.
Place the clump into the container and adjust the soil level so that the top of the clump is 1 inch from the top rim of the pot. Fill around the plant with potting mix, packing the soil down with your fingers, until the level of the soil is at the original level of the root ball.
Water the repotted plant well immediately after potting, but keep it dry for the remainder of the winter. Place your agapanthus in a sheltered location and keep it safe from freezing temperatures.