Drill holes in the mortar at all four corners of the spalled brick. The holes should be small enough to do this without touching or damaging the other bricks in the wall.
Tap in a masonry bolster between the brick and the mortar, on all four sides of the spalled brick. The mortar should start to crumble and fall out. Repeat this process with increasingly large bolsters to widen the hole around the spalled brick.
Remove the brick if it is loose enough. If it is not, continue to tap around the brick with a bolster until the brick will come free.
Line the sides of the hole with fresh mortar and allow it to sit for 10 minutes. Insert the new brick and insert more fresh mortar into the hole around the brick using a narrow tuck pointing trowel.