Here's a cement patio that was covered decades ago with slate tiles. Some along the edges have popped up. Underneath the popped tiles we can see that the slab has cracked.
What are proper and/or expedient ways to resecure these tiles to the slab?
The most likely reason for the tile popping and crack is water getting under tile and freezing. First remove old thinset and clean. I would use a roll on waterproofer like RedGard to seal concrete. Use a polymer-modified adhesive thinset rated for outside use to install slate and grout.