Tiling over broken fireplace hearth
You’ll need to determine the cause of the broken tile, or you’ll need to remove everything down to a solid base. 

The broken tiles could be from: 1) settlement, 2) heat expansion, 3) bad original installation, 4) extra heavy load applied, 5) tenant vandalism

BTW, when you add your wall base, mortar, grout, etc., make sure it’s resistant to heat. Otherwise it will sag when heated.