Remove the old crown around the flue liner using a ball peen hammer and chisel. Angle the tip of the chisel away from the liner so you don't damage it and try not to let the debris fall down the flue.
Clean the top edge of the flue liner with a wire brush and apply fireplace mortar with a caulking gun along the edge. Position a terra cotta liner extension squarely on top of the existing liner.
Build up the walls of the chimney with bricks to the height of the new liner. The wall should end about 8 inches below the top of the flue extension.
Build a form using 2 by 6's around the top of the chimney and position it around the chimney top so the form hugs the sides tightly. Pour a batch of mortar according to manufacturer's instructions into the form.
Use a masonry trowel to slope the crown up toward the flue liner as the mortar begins to stiffen. Leave about 4 inches of liner exposed.
Mist the mortar with a garden hose and tape plastic sheeting over the mortar to keep it damp for the next few days. Remove the frame when the mortar has cured.