Open the trapdoor above the lower part of this alcove by standing at the edge, facing the handle, and jumping straight up to grab it.
Pull up into the crawlspace on the left.
Crawl through and drop into the small room beyond.
Pick up a quiver of poisoned arrows.
Continue through the next crawlspace, which leads to an opening above the STREET WITH THE PALM TREE.
If you didn't do so earlier, you'll need to destroy the concrete bracket obstructing the crevice in order to progress.
To do this, turn right, crawl up the ramp a little ways, draw pistols while crouching, and shoot the bracket.
Then crawl backwards to the edge, hang, and traverse to the left along the sloping crevice. (This isn't possible without first destroying the obstacle.)
Continue traversing to the left...
...around the next two corners. Then drop onto the ledge.