Find a replacement. Ideally an original from somewhere less visible. If not then you should be able to identify it and apply for a sample (usually free or very cheap). Look at LBC for starters, it looks like it may be one of theirs but not certain. But LBC don't provide samples now, they just send a photo out - so you'll need to find somewhere you can buy one, which may be tricky but possible.
Drill around the ends and beneath repeatedly with an 8mm masonry drill bit (stitch drilling). Drill diagonally to start to merge the holes. You may find the mortar's soft enough that you can drag the drill sideways to merge the holes together, if not use a bolster. Don't touch or go near the joint above it, make the brick fall downwards, away from the DPC.
Once you've got it out, scrape the edges clean. Then gently rub away from the underside of the DPC with a gloved hand. Wash it all out with water and a hand brush. Leave it damp, if you have a break at this point then dampen it again before carrying on. Not dripping wet, but not dry either.
Put a mortar bed beneath, fill the brick's frog if it's frogged. Press mortar against one end of the hole. Butter the other end of the brick, making the fillet narrower at the back edge than the front. Hold the brick up on a trowel, guide it in unbuttered end first, then turn in the buttered end. Align the brick. Use your trowel to gently push down on its top surface until it's at the right level.
Then feed in mortar to the top edge, using two trowels to slide small sausages in at a time.